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Industry Structure and the Strategic Provision of TradeCredit by Upstream Firms∗
Alfred Lehar†
University of CalgaryHaskayne School of Business
Victor Y. SongSimon Fraser University
Beedie School of Business
Lasheng YuanUniversity of Calgary
Department of Economics
October 2019
Abstract
Trade credit can serve as a collusion mechanism for competing supply chains to increaseproducer surplus in medium concentrated industries. We analyze theoretically how theform of financing influences retailers’ behavior in the product market, study incentives todeviate and show evidence consistent with the predictions of the model. Trade credit useis inversely U-shaped in industry concentration and this pattern is more pronounced inindustries more prone to collusion and when incentives to deviate are smaller.
∗We want to thank Christina Atanasova, Mariassunta Giannetti, Pablo Moran, Clemens Otto, Robert Oxoby,Neal Stoughton, Scott Taylor, Jean-Francois Wen, Ashraf Zaman, Josef Zechner, and participants at the EuropeanFinance Association, European Economic Association, Western Finance Association, Northern Finance Associa-tion, International Industrial Organization Conference, Canadian Economic Association Conference, the Univer-sity of Vienna, Beedie School of Business at Simon Fraser University, Zicklin School of Business, Mount RoyalUniversity, and the University of Calgary. Alfred Lehar is grateful for support by the Social Sciences and Human-ities Research Council of Canada.†Corresponding author, Haskayne School of Business, University of Calgary, 2500 University Drive NW, Cal-
gary, Alberta, Canada T2N 1N4. e-mail: [email protected], Tel: (403) 220 4567.
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1 Introduction
Trade credit financing is one of the largest and most important short-term financing options
in the United States and other countries. (Cunat 2007) shows that trade credit accounts for
25% of total assets and 47% of total short-term debt for a US representative firm. Trade
credit accounts for 17% of total assets and 50% of short debt for a representative UK firm.
Yet trade credit use varies, as we will document in this paper, with the degree of compe-
tition. Figure 1 shows mean and median trade credit use, defined as receivables over total
sales, for quintiles of industry concentration for a sample of Compustat firms. Trade credit
uses peaks in medium competitive industries.
In this paper we provide an explanation for this inter-industry pattern of trade credit
use. We argue that trade credit can be used by supply chains as a collusion mechanism
which is most effective in oligopolistic industries. In our model, in the first stage supply
chains collude to use trade credit financing. To sustain collusion, firms have to coordinate
on the use but not the extent of trade credit financing. In the second stage, supply chains are
myopic and suppliers and retailers maximize profit given the form of financing. We show
that relative to financing with straight debt, trade credit influences the retailers’ behavior
in the product market and distorts product market competition. When the supply chains in
an industry all use trade credit financing, they increase producer surplus due to the changes
trade credit brings for product market competition. Trade credit financing can thus be seen
as a collusion mechanism. The increase in total producer surplus from trade credit financing
relative to bank financing depends on the degree of competition and is highest in oligopoly
markets; there is no benefit of trade credit financing for producers under monopoly or per-
fect competition. Our model thus implies an inverse U-shaped relationship between the
benefit of extending trade credit and the degree of competition.
In our empirical analysis, we confirm the inverse U-shaped pattern between competi-
tion and receivables for a sample of U.S. non-financial firms from Compustat. Consistent
with collusion being the channel for this pattern in trade credit use we find that the inverse
U-shaped pattern between competition and trade credit use is more pronounced in environ-
ments that favor collusion such as stable or declining industry growth or high barriers to
entry, when the products that firms offer are more similar, or for industries that have been
identified in the literature as being more susceptible to cartels.
The increased producer surplus of trade credit can only be realized when all firms in an
industry collude to use trade credit. Like with many collusive equilibria, given that all other
firms use trade credit, one supply chain has an incentive to deviate and use bank financing
for a short-term gain. For example, financially flexible retailers can deviate by paying off
trade credit obligations with set-aside cash in bad states of the world. Consistent with our
2
model we find the inverse U-shaped pattern to be less pronounced among firms with large
cash holdings. We compare a one-time benefit of deviation to the benefit of sustaining
the collusive trade credit equilibrium and derive conditions under which deviation is not
optimal. Comparing trade credit as a collusion mechanism to classic collusion where output
quotas are allocated to cartel members, we find that collusion via trade credit is easier to
maintain in most cases. Instead of having to coordinate on often unobservable prices or
quantities the collusion mechanism in this paper only relies on all firms offering trade credit
to their retailers, which is much easier to police by other cartel members. We also document
why trade credit relies on the supplier-retailer relationship and cannot be easily replicated
by a competitive banking sector.
As further evidence consistent with the predictions of our model we find that the inverse
U-shaped pattern is more pronounced in industries with high demand volatility. We extend
our baseline model to allow for a simple bargaining game between the supplier and the
retailer; the model predicts that increased retailer-bargaining power decreases the benefit
of trade credit financing as most of the surplus that the retailer can extract gets competed
away in the product market. Consistent with this prediction we find that the inverse U-
shaped pattern is more pronounced when downstream industry concentration is low.
Trade credit influences product market competition because of the different structure
of interest payments. In contrast to straight debt where interest is proportional to the time
money is borrowed under trade credit financing, retailers borrow goods from their suppliers
free of charge for a certain period of time and have to pay a very high interest rate, set by
the supplier, should they need to extend their financing. When demand is high and the
retailer can sell his whole inventory within the free financing period, the retailer does not
have to make any payments for financing the inventory. When demand is low, however, the
trade credit penalty rate, at which leftover inventory has to be financed, will influence the
retailers optimal behavior in the product market. Therefore, trade credit penalty rate can be
used strategically by the supplier to influence her retailer’s state contingent behavior in the
retail market.
To illustrate our intuition how trade credit financing alters competition suppose two
supply chains in the car industry collude to use trade credit financing. Two competing car
producers each supply one car dealership in a city facing uncertainty about demand for cars
by local residents. The car manufacturer provides trade credit to the dealership under which
the latter gets free financing when they sell all cars this period but face a high interest rate
for financing all cars that the dealer rolls over for sale in the future. When ex-post realized
consumer demand is low the dealer has to roll over some inventory for sale in the next
period. Yet for every additional car that he sells this period he can save the high financing
3
costs from the trade credit contract. Thus, he will optimally be more aggressive in the
market. This period he will sell more cars at a lower price compared to the outcome of a
standard Cournot model and obtain a lower profit.
Ex-ante, before consumer demand is realized, the dealer anticipates that he could end
up in the unprofitable low demand state, facing low sales and high financing costs, and he
therefore orders a smaller inventory from the manufacturer. Thus, when consumer demand
turns out to be strong, he is constrained by his inventory and can only supply a limited num-
ber of cars to the market. Because the two supply chains collude, his competitor follows the
same inventory policy and has only limited supply as well. Prices for cars are, due to the
limited inventory of both dealers, higher than in a standard Cournot game and dealers can
earn large profits.1 We show that these distortions that trade credit financing creates in the
product market competition result in higher combined expected profits for the manufacturer
and the dealer compared to straight debt financing.
While it is hard to observe actual trade credit or floor plan financing contracts, we can
find anecdotal evidence, mostly from court cases, that is consistent with our idea that sup-
pliers want to influence retailer behavior. A home appliance retailer2 obtained a floor plan
financing contract with a free financing period of three to six months after which the rate
would jump to 18%. The court notes that ‘... the free floor plan program created an interest-
free span of time which served as an incentive for a dealer to rapidly sell his inventory and
pay off his obligation to the company. If the dealer failed to dispose the merchandise within
the designated time, he was penalized for not moving it quickly enough...’. A similar in-
centive program by Fiat motors offered a 120 day free financing period.3 A recent industry
publication notes that car dealerships can take ‘...advantage of programs in which factories
repay them for interest [of inventory financing]. By selling a vehicle faster than a factory-
set target number of days, which varies by manufacturer, a dealer can actually make money
on floorplanning.’4
The discrete jump in the interest rate that the manufacturer charges after the free financ-
ing period, which is unique to trade credit financing, is essential for the mechanism of our
model. (Ng, Smith, and Smith 1999) report that typical payment terms are industry specific;
most firms in their survey claim to demand payment within 30 days. Examining actual trade
credit contracts (Klapper, Laeven, and Rajan 2012) document that payment terms are often
much longer and suppliers provide free financing in that period. Late payment penalties
1(Zettelmeyer, Morton, and Solva-Risso 2007) find that car dealers earn scarcity rents when demand for cars ishigh.
2Romine vs. Philco Finance Corporation, United States Court of Appeals, Eighth Circuit, No 76-1535, 1977.3Fiat Motors of North America vs. Mellon Bank, United States Court of Appeals, Third Circuit, Nos 86-3588
and 86-3606, 1987.4Jamie LeReau, Interest spike would trim inventories, Automotive News, July 15, 2013.
4
0.19
0.18
0.17
0.16
0.15
0.14
20% 40% 60% 80% 100%
Mean
Median
Tradecredituse:Receivables/TotalSales
Quantile HHI
Figure 1. Trade Credit use and industry concentrationThe graph shows the mean (solid line) as well as the median (dashed line) of receivables over total salesfor quintiles of industry concentration as measured by the Herfindahl-Hirschman Index of sales (HHI)based on Compustat data.
arise either explicit, when the buyer pays the invoice after the payment due date, or im-
plicit, when the payment is made after the discount period. Late payment penalty rates are
usually very high; in the EU, for example, the Late Payments Directive 2011/7/EU enacts
8% plus a (central bank) reference rate as contractual default penalty rate. Indirect penalties
arise when firms miss the discount period. For example, the commonly quoted scheme of
2/10 net 30 means that the retailer has to pay 2% more if he pays within 30 days rather
than the first 10 days, which is equivalent to an annual interest rate of around 46%—a huge
penalty for the delayed payment (see also (Smith 1987), (Ng, Smith, and Smith 1999), and
(Petersen and Rajan 1997)). Using actual contracts (Klapper, Laeven, and Rajan 2012) find
that for 30% of the two-part contracts in their sample, the discount period ends exactly one
day before the payment due date imposing a huge penalty for paying late. Economically,
under both commonly found payment terms, suppliers provide a period of free financing
combined with a high rate imposed on late payments. We argue that the high interest rate
only applies when demand is low and inventory gets rolled over and can thus be seen as a
state contingent financing cost that allows the supply chain to fine tune the retailer’s opti-
mal state contingent product market strategy. When all supply chains in an industry alter
competition by using trade credit they can increase producer surplus.
We contribute to the existing literature in three ways: First, we show that trade credit can
be used as a collusion mechanism in oligopolistic industries. Compared to classic collusion
mechanisms that require coordination on unobservable output quantities or prices, trade
credit only needs implicit agreement on the use of trade credit, which is easy to verify for
other cartel members. Second, we document a link between trade credit use and industry
structure. In line with the predictions of our model we find that trade credit use is higher in
5
medium concentrated industries, industries that are more prone to collusion when incentives
to deviate are smaller, and when downstream industry concentration is low. Third, we
provide a novel justification for the specific structure of trade credit which differs from
traditional debt. The two-tier rate structure with free financing for a certain period followed
by a very high interest rate create the distortions in the product market competition that will
allow colluding supply chains to extract more producer surplus.
Our research relates to recent papers on trade credit and competition. (Chod, Lyandres,
and Yang 2019) analyze a free riding problem in trade credit financing with multiple sup-
pliers that arises as each supplier wants to provide trade credit financing only for her own
product but can end up subsidizing other suppliers. In their setting, providing trade credit
financing is costly for the supplier. (Singh 2018) documents that Indian manufacturing
firms use trade credit as strategic tool to defend market share and deter entry by rival firms.
We focus on a different channel to document how trade credit can influence product market
competition for the purpose of collusion which fits into a recent stream of research on col-
lusion and finance. (Azar, Schmalz, and Tecu 2018) and (Azar, Raina, and Schmalz 2016)
analyze how common ownership decreases competition in the airline and banking industry,
respectively. (Lyandres, Fu, and Li 2016) analyze competition among underwriters in IPOs.
A related stream of research analyzes the interaction of financial structure and product
market competition that builds on (Brander and Lewis 1986). They show that debt financ-
ing makes firms with limited liability more aggressive in Cournot competition. A rich
literature examines the empirical relation between leverage and capital structure. (Phillips
1995) documents that in three out of four industries studies output decreases in leverage.
(Kovenock and Phillips 1997) document that debt increases in concentrated industries are
associated with plant closures and reduced investment. Using data on the casino indus-
try (Cookson 2017) documents low leverage incumbents can successfully deter entry with
capacity expansion while highly levered ones do not expand capacity in response to entry
threats. While most of the work in this field examines how levels of debt change firms’
behavior in imperfect competition, our paper analyzes how different types of debt affect
firms’ behavior in a strategic setting.5 Our approach also differs because we do not utilize
default or conflicts between shareholders and bondholders in our model.6
Our paper relates to the broader trade credit literature (see (Petersen and Rajan 1997) for
5Another stream of research relates industry structure to debt maturity - another dimension of debt structure.(Xu 2017) documents that firms with low credit rating frequently refinance outstanding bonds before maturity toextend the maturity of their debt, while investment grade firms do not manage maturity this way. (Parise 2018) findthat incumbents in the airline industry increase debt maturity as a response to increased threats of entry.
6Our paper is also related to the huge literature on contracting and competition in vertical relationships basedon (Hart and Tirole 1990) and to papers identifying other mechanisms for price discrimination such as resale pricemaintenance (e.g. (Chen 1999)), or slotting allowances (e.g. (Shaffer 1991)).
6
a survey).7 (Uchida, Udell, and Watanabe 2013) document that trade credit use is increasing
in the length of a relationship between small firms and their suppliers even when many
other financing resources such as short- and long-term bank loans are available. Our paper
is also close to the work of (Brennan, Maksimovic, and Zechner 1988). In their model, a
producer price-discriminates between consumer types. Low type consumers finance goods
with expensive trade credit but default with a high probability on their debt, effectively
making a low expected payment to the vendor. High type customers never default and
prefer to pay cash to avoid the high interest rate, and thus pay an ex-ante higher price for the
good. In our model, suppliers use trade credit to effectively charge different prices across
demand states for the purpose of collusion. The mechanism in our model also requires no
default.
Predictions of our model are also consistent with the findings of previous empirical
studies. Analyzing provision of trade credit of Indonesian suppliers, (Hyndman and Serio
2010) find a hump shaped pattern as predicted by our model with a very sharp increase
in trade credit provision when moving from monopoly to duopoly. Their paper, however,
analyzes the optimal strategy of a revenue maximizing supplier facing credit contained and
unconstrained buyers in the presence of monitoring costs for trade credit. Our predicted
positive relationship of trade credit use and competition in highly concentrated markets is
consistent with the findings of (Fisman and Raturi 2004), who examine supply chain rela-
tionships in five African countries and find that monopoly power is negatively associated
with credit provision. Our predicted negative relationship of trade credit use and competi-
tion in more competitive markets is consistent with (McMillan and Woodruff 1999), who
find trade credit to decrease as competition intensifies for a sample of Vietnamese firms,
and (Giannetti, Burkart, and Ellingsen 2011), who find that sellers of differentiated goods,
which are subject to less competition, carry higher receivables than producers of homoge-
neous goods.
7Previous studies point out that suppliers have a comparative advantage to control their retailers (suppliers canstop supplying goods to retailers, see (Cunat 2007); it is easier for suppliers to re-possess collateral than banks, see(Frank and Maksimovic 2005); suppliers also have an informational advantage relative to outside financiers since itis less costly for suppliers to monitor retailers’ financial status ((Jain 2001)). In addition, trade credit can mitigatea moral hazard problem on the side of retailers ((Cunat 2007) and (Burkart and Ellingsen 2004)), trade creditmight also serve as a quality-guarantee mechanism for intermediate goods ((Lee and Stowe 1993), (Long, Malitz,and Ravid 1993)), relaxes budget constraint due to the possibility of a postponed debt payment ((Ferris 1981)),and help retailers overcome credit rationing problems if asymmetric information makes banks unwilling to lendto retailers ((Biais and Gollier 1997)). (Allen, Qian, and Xie 2019) examine trade credit in the more generalcontext of informal financing. (Peura, Yang, and Lai 2017) study trade credit in Bertrand competition with random,exogenous liquidity shocks. Under trade credit financing firms split the market to improve their liquidity. We focuson collusion and abstract from financial constraints. (Liang and Qin 2017) analyze revenue sharing agreementsand fairness in supply chains. (Tang, Yang, and Wu 2017) model trade credit as mechansim to mitigate suppliermoral hazard.
7
2 Baseline model
In this section of the paper we present the basic model and solve for the product market
equilibrium for a given form of financing. The optimal choice of financing will be discussed
in Section 4.
We consider an infinitely repeated three-stage game in which n supply chains produce
and sell a homogeneous, non-depreciating good to consumers. We assume that each supply
chain consists of one supplier and one retailer, who sells the product in a local market.8
Consumer demand is either high (good state) with probability q or low (bad state) with
probability 1− q. The price in the product market is given by As −Q, where the intercept
is state dependent and Q denotes aggregate quantity supplied to the market. Our model can
be seen as a special case of a double marginalization problem.
In stage 1, at the beginning of each period, each upstream supplier chooses whether to
supply trade credit or not and given the financing scheme (bank financing or trade credit
financing), sets a wholesale price P for the good as well as the trade credit interest rate rs,
if applicable. Suppliers can produce unlimited quantities of the good at zero marginal cost.
In stage 2, each retailer orders goods from his own upstream supplier to fill his inventory,
taking the price (and trade credit interest rate if applicable) as given. We assume that each
retailer can only purchase inventory from their own supplier and vice visa. In stage 3, at
the end of each period, consumer demand is realized and retailers sell their goods to the
product market, competing in quantity.
The key friction that we assume is that a retailer cannot acquire inventory from his
supplier instantly (e.g. goods take time to build or require transportation); each retailer’s
end of period sales are therefore bound by his inventory. However, retailers can store any
unsold inventory for the next period at no cost, except financing costs. We assume retailers
to have zero fixed costs. To simplify the exposition of the paper and to create a need for
financing we assume that profits are distributed to shareholders at the end of each period so
that retailers require external financing for their inventory. This assumption can be relaxed
without changing the findings of the model. Our results hold as long as the marginal good
sold in the bad state is financed externally.
The purpose of our paper is to show the impact that trade credit financing has on product
market competition.9 We analyze product market competition under two external financing
8In reality a supplier, e.g. a car manufacturer, will have a global network of multiple retailers in many markets.We focus on the effect of trade credit as mechanism to influence product market competition between retailers andfor simplicity we analyze the situation with only one retailer. The supplier could have retailers in other marketswhich would not change our findings as long as these markets are separated. Alternatively, we could interpret themodel as each supplier having a representative retailer in a region.
9Other contracts might also influence competition. It is not the purpose of our paper to find the optimal contract
8
mechanisms for the retailers, straight debt provided by a competitive banking sector (or
a bond market) and trade credit financing offered by their own suppliers. Under bank
financing, the retailer pays the supplier in cash at the time of the order and finances the
inventory with a bank. Since retailers have no fixed costs and are on average profitable, they
will never default and can thus borrow at the risk-free rate. Under trade credit financing,
the retailer gets free financing from the vendor for the goods that are sold at the end of the
period, while he has to pay the trade credit interest rate rs, which is optimally chosen by
the supplier, to finance any unsold inventory that is rolled over to the next period. In this
infinite horizon game, the end of the current period equals the beginning of the next period.
We assume that all agents are risk neutral.
To rule out trivial solutions we assume that the demand state is observable but not con-
tactable. This assumption has two important implications: first, it prevents suppliers from
directly charging demand state contingent prices to their retailers. In the U.S., for example,
the Robinson-Patman Act prevents suppliers to price discriminate against their retailers.10
Suppliers might, in reality, also be poorly informed about changes in local demand to cre-
ate an effective system of price discrimination. Second, in our model, retailers cannot write
state contingent financing contracts with the bank. Such contracts are not observed very
often in practice, we would argue because it is very hard to verify the demand state in
court.11
The retailer will offer fewer goods in the bad state when the choke price decreases. To
rule out a corner solution in which the retailer offers zero goods in the bad state and only
sells in the good state we impose a lower bound on the choke price in the bad state, Ab,
between supplier and retailer. In Section 5.5 and in Appendix E we discuss why the trade credit contract cannot bereplicated by a competitive banking sector.
10In 1994, for example, the American Booksellers Association and independent bookstores filed a federal com-plaint in New York against several publishers alleging that they offered more advantageous promotional allowancesand price discounts to certain large national chains and buying clubs. Eventually, seven publishers entered consentdecrees to stop predatory pricing.
11The assumptions of our model rule out several other theories of trade credit in the literature. In (Murfinand Pratt 2019) financing provided by a monopolist producer to consumers serves as commitment device to keepprices high over time. In their model the producer competes with herself over time in the presence of a usedgoods market. We do not allow for used consumer goods to directly compete with newly produced goods andwe focus on wholesale rather than consumer financing. In our model retailers and consumers never default whichis central to the price discrimination in (Brennan, Maksimovic, and Zechner 1988). We rule out liquidity shocks(as e.g. in (Cunat 2007)), financial constraints (e.g. (Petersen and Rajan 1997)), or the need to support a retailerto maintain a profitable business relationship ((Wilner 2000)). In our model we do not require that the supplierhas some advantage over the bank in liquidating collateral (e.g. (Frank and Maksimovic 2005) or (Longhofer andSantos 2003)), in our setting no player has an incentive to default strategically ((Burkart and Ellingsen 2004)), andthere is no asymmetric information (e.g. (Biais and Gollier 1997)).
9
which ensures that non-negative sales occur in both states (see also footnote 14):
Ab ≥2Agq
2q + n+ 1(1)
2.1 Solution
Our model is a dynamic game with demand uncertainty and the solution could be path
dependent as current orders depend on last period sales and inventory levels. As we will
show below, because of the infinite horizon, we are able to rearrange the cash flows and
inventory valuation in such a way that each period is identical. With identical periods, one
possible, not necessarily unique strategy that maximizes the overall expected profit, is to
maximize the profit in each period. We therefore solve the game as a time independent
static game, which is much more tractable. We will explain our approach in more detail
in the following subsections. We solve for the equilibrium by backward induction starting
with the retailers’ decision problem.
2.1.1 Stage 3: The retailer’s end of period problem – ex-post competition
At the end of the period, each retailer i maximizes its profit ωi by competing in quantity
Qfs given the demand state s, the chosen form of financing f , and the amount of inventory
If obtained before the state of the demand is realized. Superscript f ∈ {B, T} indicates
a retailer’s financing choices, either bank financing (B) or trade credit financing (T ); sub-
script s ∈ {b, g} denotes the demand states, either a good state (g) or a bad state (b). In a
bad state, the choke price isAb; in a good state, the choke price is Ag, where Ag > Ab. The
retailer’s problem is
maxQfs
ωfs = (As −Qfs −Q−i,fs )Qfs − Cfs , f ∈ {B, T}; s ∈ {b, g} (2)
s.t. Qfs ≤ If (3)
where Q−i,fs is the aggregate quantity offered by the other retailers except i and Cfs is the
retailer’s total cost measured in the end of period values. The total cost for the retailer
includes the purchase cost of the good as well as the financing cost of keeping the good in
inventory until it is sold. Holding excess inventory is costly under both forms of financing
and therefore the retailer will never optimally hold more inventory than what he sells in the
good state. In the good state, the constraint (3) is therefore binding and Qfg = If . We solve
the third stage game assuming the inventory constraint to be binding in good states and not
binding in bad states and later verify that this assumption is indeed true.
10
Table 1. State dependent inventory levels, cashflows, and financial obligations for the retailer under bank(panel A) and trade credit financing (panel B), respectively.
Panel A: Bank FinancingGood state Bad state
Inventory CF Retailer Loan balance Inventory CF Retailer Loan BalanceStarting balance Qg QgP Qg QgPSale −Qg QgPm −Qb QbPm
Repay loan −QgP −QgP −QbP −QbPInterest −rQgP −rQgPRestock inventory Qg QgP Qb QbP
Ending balance Qg ωg QgP Qg ωb QgPPanel B: Trade Credit Financing
Good state Bad stateInventory CF Retailer payables Inventory CF Retailer payables
Starting balance Qg QgP Qg QgPSale −Qg QgPm −Qb QbPm
Repay supplier −QgP −QgP −QbP −QbPInterest 0 − rs
1+r (Qg −Qb)P
Restock inventory Qg QgP Qb QbPEnding Balance Qg ωg QgP Qg ωb QgPBy allocating cashflows and valuing inventory as presented in the tables we make inventory levels and financialobligations at the beginning of the period independent of the state in the previous period. The total cash flow at theend of the period only depends on this period’s demand state that is realized in that period. Qg and Qb denote thequantity sold in the good state and the bad state, P denotes the wholesale price charged by the supplier, Pm is theprice achieved in the retail market, and ωg and ωb are the retailer’s profit in the good and bad state, respectively.All superscripts, which are used to indicate bank financing or trade credit financing throughout the text, are omittedfor simplicity.
We analyze the bank financing case first. The retailer’s profit in the bad state is
ωBb = (Ab −QBb −Q−i,Bb )QBb − PQBb − PQBg r, (4)
where the first term is the revenue from selling QBb units to the market, the second term is
the cost of restocking the inventory at a cost of PB per unit and the third term is the cost
of financing the inventory with value PBQBg at the bank rate r. The retailer’s profit in the
good state is similar except that he sells the whole inventory QBg for a total profit of
ωBg = (Ag −QBg −Q−i,Bg )QBg − PQBg − PQBg r. (5)
Panel A in Table 1 provides an overview of a retailer’s cash flows and inventory levels under
bank financing. Our model would also work if the retailer used a part of his profit to reduce
his debt by more than PBQBb to save on future financing costs as long as the marginal unit
sold in the bad state is still financed with debt. Our debt repayment policy is consistent with
industry practice. For example, the U.S. Small Business Administration defines floor plan
financing as ”Floor plan financing is a revolving line of credit that allows the borrower to
11
obtain financing for retail goods. These loans are made against a specific piece of collateral
(i.e. an auto, RV, manufactured home, etc.). When each piece of collateral is sold by the
dealer, the loan advance against that piece of collateral is repaid.”12
Now we turn to analyze the trade credit financing case as shown in Panel B of Table 1.
The retailers profit in the bad state is
ωTb = (Ab −QTb −Q−i,Tb )QTb − PQTb − P T rs(QTg −QTb )/(1 + r), (6)
where again the first term is the revenue, the second term is the cost of restocking the
inventory at a cost of P T per unit. The third term is the cost of financing any leftover
inventory with value P T (QTg −QTb ) at the trade credit penalty rate rs. Since the trade credit
interest payment is due only next period it gets discounted by one period. The retailer’s
profit in the good state is similar except that there are no financing costs as he sells the
whole inventory QBg within the free financing period for a total profit of
ωTg = (Ag −QTg −Q−i,Tg )QTg − PQTg . (7)
As noted above in a good state the constraint (3) is binding and the sales are constrained
by the inventory If which is determined in stage 2. In a bad state, however, the constraint
is not binding and the first order conditions to solve for the optimal quantity offered by
the retailer are derived from Equations (4) and (6) for bank financing and trade credit,
respectively. In Appendix A we derive the first order conditions and the optimal quantity
of sales in the bad state.
2.1.2 Stage 2: The retailer’s start of period problem —ex-ante inventory de-cision
Given the price of the good, P f (and trade credit interest rate, rs, if applicable) set by each
supplier, each retailer makes an ex-ante inventory decision to maximize their expected total
profits. No cash flows occur for the retailer at the beginning of the period because inventory
is externally financed either through straight debt or through trade credit financing. As il-
lustrated in Table 1 retailers enter and exit each period with the optimal inventory level and
payment obligations either to the bank or to the supplier independent of the demand state
in the previous period. We can therefore transform the potentially complex dynamic opti-
mization problem to a state-independent static optimization problem in which all periods
are ex-ante identical.12see U.S. Small Business Administration, Special Purpose Loans Program, http://www.sba.gov/content/what-
floor-plan-financing
12
To determine the inventory and thus the sales quantity in the good state the retailer
maximizes the expected payoff, which is the probability weighted average of the retailers
profit in the good state, ωfg , and in the bad state, ωfb , respectively. Given the sales quantity
in the bad state, Qfb , as the solution of the optimization problem (2), the retailer maximizes
his expected profit ωf to determine inventory and thus sales in the good state Qfg .
maxQfg
ωf =[(1− q)ωfb + qωfg
]f ∈ {B, T}, (8)
2.1.3 Stage 1: The supplier’s problem
Given the optimal inventory policy of the retailer the supplier sets the price (and the trade
credit interest rate, if applicable) to maximize her profit. We again structure cash flows
such that each period is identical for the supplier and examine the strategy to maximize
each period’s profit, πf , as one way to maximize her overall profit.
Under bank financing, the supplier only has the wholesale price as a choice variable to
maximize her expected profit
maxPB
πB = (1 + r)PBQBg − (1− q)PB(QBg −QBb ) (9)
When sellingQBg goods to their retailer, the supplier immediately obtains the cash payment,
which will be worth (1 + r)PBQBg at the end of the period. However, with probability
(1− q) a bad state will occur and the retailer will buy fewer goods when re-stocking for the
next period as he keeps Qg −Qb goods in hand. Thus, the supplier will lose in expectation
(1− q)PB(QBg −QBb ).Under trade credit financing, each supplier maximizes the expected profit through si-
multaneous choice of price P T and trade credit interest rate rs.
maxPT ,rs
πT = qP TQTg + (1− q)
(P TQTb +
rsPT (QTg −QTb )1 + r
)(10)
With probability q a good state occurs and each supplier obtains a cash payment of
P TQTg at the end of the period for all the goods she has lent to the retailer. With probability
(1 − q) a bad state occurs and each supplier gets paid for the sold goods P TQTb in the
current period and collects the penalty payment in the next period, which has a present
value of rsP T (QTg −QTb )/(1 + r).
Given the solutions for the optimal sales quantities for the good and the bad states from
the optimization problems (2) and (8), respectively, we can determine the suppliers optimal
wholesale price under bank financing by solving problem (9). Similarly, under trade credit
13
financing we can find the optimal wholesale price and trade credit interest rate by solving
the optimization problem (10). To simplify the exposition of the paper, we focus for most
of the remaining analysis of the baseline model to the case when the risk free rate goes to
zero.13 The following propositions summarize the game solutions for bank financing and
trade credit financing, respectively.
Proposition 1 There exists a subgame perfect Nash equilibrium under bank financing such
that each supplier charges PB =2(qAg+(1−q)Ab)
3+n , each retailer orders an inventory QBg =(3+n−2q)Ag−2(1−q)Ab
(n+3)(n+1) , and sells QBg in a good state and QBb =2qAg+(1+n+2q)Ab
(n+3)(n+1) in a bad
state, respectively.14
Proposition 2 There exists a subgame perfect Nash equilibrium under trade credit financ-
ing such that each supplier charges P T =2(qAg+(1−q)Ab)
3+n and sets the trade credit interest
rate at rs =q(Ag−Ab)
qAg+(1−q)Ab , each retailer orders an inventory QTg =Agn+3 , and sells QTg in a
good state and QTb = Abn+3 in a bad state, respectively.
We can immediately see that the form of financing has an effect on the quantities firms
offer and thus will influence the overall profitability of the firms in the supply chain. It
is also noteworthy that the trade credit interest rate is always positive as Ag > Ab by
assumption.
The expected quantity sold is identical under both forms of financing as the risk-free
interest rate goes to zero. In Appendix D, however, we show numerically that with positive
interest rates expected, sales under trade credit financing are larger than under bank financ-
ing for a large region of the parameter space. This finding is consistent with the empirical
results of (Breza and Liberman 2017) who document that an exogenous restriction on trade
credit for selected firms resulted in a reduced probability of trade of affected suppliers to a
major supermarket.
13Our results with one exception also hold for a positive risk free rate but the expressions are significantlymore complex without providing any major insights. When the risk free rate r is too high holding inventoryunder bank financing is very costly for the retailer and at some point, when r > r∗ := q(Ag − Ab)/Ab > 0,optimal inventory and thus sales in the good state under bank financing are less than under trade credit financing.For this reason, the results of Proposition 3 only hold as long as r < r∗ while the other findings of the paperhold for any positive interest rate. The corresponding condition for Equation (1) with positive interest rate isAb > (2Agq(q + r))/(2(n + 3)qr + q(n + 2q + 1) + (n + 3)r2). A Mathematica workbook with the solutionsfor the general case is available from the authors upon request. Wholesale prices are independent from the form offinancing only when the risk-free rate goes to zero.
14Requiring QBb ≥ 0 yields assumption in Equation (1).
14
3 Financing choice and product market behavior
In this section, we first illustrate how financing choices affect a retailer’s behavior in imper-
fect competition, how they affect profits, and why both suppliers and retailers prefer trade
credit to bank financing.
3.1 The retailer’s decision in the bad state
We start with examining the retailer’s marginal financing cost in the bad state. Under bank
financing, the marginal financing cost is zero in a bad state, because the financing cost
depends only on the inventory level and is independent of the retailers sales decision in the
bad state. Under trade credit financing, however, the value of any unsold inventory has to
be financed at the trade credit interest rate rs. Selling an additional good saves the trade
credit interest payment which is due at the end of next period. Since rs > 0, the marginal
financing cost is negative, −P T rs/(1 + r). Trade credit financing therefore effectively
lowers the marginal cost for the retailer in bad states and makes him more aggressive in
sales. By changing the trade credit interest rate, the supplier can thus strategically influence
the retailer’s aggressiveness in a bad state.
3.2 The retailer’s inventory decision and behavior in a good state
The trade credit penalty also affects the retailer’s behavior in a good state through the
ex-ante inventory decision. We present the main intuition in this section, a more formal
exposition and a discussion of how trade credit allows the supplier to price discriminate
against the retailer can be found in Appendix H.
Adding an extra unit to inventory will enable the retailer to sell this extra unit in the
good state but it will also increase inventory financing costs. Since the inventory must be
financed in both demand states the retailer must trade off the marginal revenue of selling
an extra unit in the good state with the financing costs in both states. Consider the case of
bank financing conditional on the good state: the marginal revenue is offset by the financing
cost in the good state, which is rPB , but also by the financing cost that the extra inventory
causes should the bad state be realized, which is 1−qq rPB . The total marginal financing cost
conditional on being in the good state is therefore rPB 1q . The friction that the inventory
has to be ordered before the state is realized implies that any marginal revenue in the good
state has to offset the inventory holding cost in both good and bad states. The inventory
constraint (3) is therefore always binding in the good state, i.e. retailers would never hold
excess inventory. Higher marginal costs also imply that competition is softened in the good
state.
15
Under trade credit financing the marginal cost of adding a unit of inventory is zero in
the good state as the retailer obtains free financing for one period. Yet when the retailer
chooses inventory, he has to factor in the penalty financing costs should the bad state occur.
Total marginal financing costs conditional on being in the good state are then rs(1+r)
1−qq P T ,
which is the product of the current period value of the trade credit penalty, the ratio of the
probabilities of the bad and the good state, and the value of another unit in the inventory,
respectively. Under trade credit financing the supplier can fine tune the retailer’s marginal
financing cost and thus his behavior in the product market by adjusting the trade credit
penalty rate rs, while under bank financing the interest rate r is exogenously given. In most
cases the supplier will set the trade credit penalty rate such that the marginal costs for the
retailer are higher compared to bank financing, further softening competition in the good
state.
We summarize the above results in the following proposition.
Proposition 3 Under trade credit financing, the retailers’ marginal cost is lower (higher)
in the bad (good) state, competition is intensified (softened), and aggregate state contingent
supply increases (decreases) relative to bank financing.
3.3 The trade credit interest rate
From Proposition 2, we know that the trade credit interest rate is rs =q(Ag−Ab)
qAg+(1−q)Ab as r
goes to zero, which has several noteworthy properties: First, rs is always positive, i.e., the
solution is consistent with the empirical facts that the retailers have to pay a penalty rate if
they cannot repay their suppliers on time. Second, rs increases when a good state becomes
more significant (q or Ag − Ab is high) or a bad state is less significant (Ab or 1 − q is
low). As the relative importance of the good state increases, protecting the good state profit
(softening the competition) becomes more important, which requires a rise in rs.
Corollary 1 Under trade credit financing, the penalty rate rs increases with the probability
of a good state and the gap of choke prices in both states.
4 Financing choice and industry structure
We now look into the incentive of a supplier to offer trade credit financing, the effect of
industry structure, and the producer surplus.
From Proposition 3 we know that under trade credit competition increases in the bad
state relative to bank financing as retailers want to avoid the penalty payment, thus lowering
16
2 3 4 5 6 7 8
30
40
50
2 3 4 5 6 7 8
-20
-10
10
20
30
RetailPrice
∆ExpectedProducerSurplus
number of firms n number of firms n
IM good
IM bad
TCgood
Bank good
Bankbad
TCbad
n∗b
TC beneficial in bad state
n∗g
TC beneficial in good state
good state
badstate
good+bad state
Figure 2. Decomposition of the benefit of trade credit by stateRetail prices for the integrated monopolist (IM) and under bank financing and trade credit (TC) financingas a function of number if supply chains for the good and the bad state, respectively (left panel). Dif-ference in the expected producer surplus between bank and TC financing for the good and the bad state,respectively, as a function of the number of supply chains in the industry (right panel). The parametersfor the graph are, unless otherwise specified: Ag = 100, Ab = 70, q = 1/2, r = 0.05.
prices in the retail market. In the good state competition is softened under trade credit due
to retailers’ optimal choice of smaller inventories, causing retail prices to be higher than
under bank financing. The left panel of Figure 2 shows the relationship between retail
prices and industry concentration for bank and trade credit financing, respectively.
The graph also shows the retail price that an integrated monopolist (IM) would set in
each state to maximize producer surplus. Depending on the number of supply chains in an
industry, n, either the retail price under trade credit financing or under bank financing is
closer to the optimal price of the integrated monopolist. In the bad state, retail prices under
trade credit financing are closer to the integrated monopolist’s when industry concentration
is high (low n). In contrast, in the good state retail prices under trade credit financing are
closer to the integrated monopolists when industry concentration is low (high n). Assume
for now that n is continuous and denote as n∗g and n∗b the number of supply chains where
the retail prices under trade credit and bank financing are equidistant from the integrated
monopolist’s price in the good and bad state, respectively (see Appendix F for a formal
derivation of the results in this section). The financing mechanism that results in retail
prices being closer to the one of the integrated monopolist, will also create a higher producer
surplus.
Trade credit is beneficial in the bad state whenever n is below n∗B and is beneficial in the
good state whenever n > n∗g. We show that n∗g ≤ n∗b and hence for most parameter values
there are three regions of the parameter space.15 For medium concentrated industries with
15For most parameters n∗b is finite but it can diverge to infinity. Yet the overall benefit of trade credit alwaysdeclines in n as the economy approaches perfect competition.
17
n∗g ≤ n ≤ n∗b trade credit is most beneficial as it increases producer surplus in both states.
For industries with n < n∗g or n > n∗b the gains of trade credit in one state are offset with
losses in the other state. This intuition generalizes and we find that for the supply chains
the relative advantage of trade credit financing over bank financing is inversely U-shaped
in industry concentration. The following proposition formalizes this intuition.16
Proposition 4 The difference in expected producer surplus per supply chain between trade
credit financing and bank financing is an inverse U-shaped function in the number of supply
chains.
The right panel of Figure 2 shows the difference between the producer surplus under
the two forms of financing by state as well as the combined effect. When the number
of supply chains is low, benefits from trade credit financing are realized in the bad state
as the increased aggressiveness induced by trade credit financing shifts retailers’ optimal
behavior closer towards the first best, i.e. the integrated monopolist. As the number of
supply chains increases, the benefit of trade credit comes predominantly from the good
state as competition drives down retail prices and the less aggressive retailers, under trade
credit financing, keep retail prices closer to the ones of the integrated monopolist. With at
least two supply chains the benefit of trade credit in the good state generally outweighs the
cost in the bad state and trade credit allows the supply chains to increase producer surplus.
This gain comes at the expense of consumers. This intuition is summarized in the following
proposition.17
Proposition 5 In imperfect competition expected consumer surplus is lower under trade
credit financing than under bank financing. With at least two supply chains the expected
producer surplus per supply chain is higher under trade credit financing.
5 Stability of the collusive mechanism
In our model, trade credit financing is a collusion mechanism that allows producers to
extract rents from consumers. However, like for most other collusion mechanisms there
exists an incentive for firms to deviate from the collusive equilibrium for short-term gain. In
this section we will analyze possible deviations from the collusive equilibrium and compare
trade credit as a collusion mechanism with classic collusion based on output coordination.
16Appendix I provides a more detailed example of how trade credit finance changes marginal costs and producersurplus.
17Within the confined setting of our model we can show that total welfare under trade credit financing is alsolower than under bank financing.
18
4 6 8 10 12 14
0.03
0.04
0.05
0.06
0.07
0.08
0.02 0.04 0.06 0.08 0.10
2.4
2.6
2.8
3.0
3.2
3.4
Expectedprofitdeviating/producersurplus
Number of Firms in Industry
Number
ofrequired
punishmentperiods
Risk free interest rate r
q = 1/2
q = 1/4
q = 3/4
n = 3
n = 10
n = 5
Figure 3. Deviation of a supply chain form the trade credit equilibriumShort term gain as a fraction of producer surplus for a supply chain to deviate to bank financing given thatthe other supply chains stick with trade credit financing for different probabilities of the good state q (leftpanel). Number of periods that players must be committed to play the bank financing equilibrium after adeviation by one firm to deter deviations from the trade credit equilibrium (right panel). The parametersfor the graph are: Ag = 100, Ab = 60, q = 1/2, r = 0.05.
5.1 Deviations of a supply chain
One way to deviate is that a whole supply chain might move from trade credit financing
to bank financing. To analyze the robustness of trade credit as a collusion mechanism in
our paper, we numerically analyze the incentives to deviate. We extend the baseline model
to allow m < n supply chains to finance retailers’ inventory with bank financing while
the other n−m firms use trade credit financing (see Appendix B). We allow retailers that
use bank financing to offer different quantities than retailers under trade credit financing
and similarly allow suppliers to offer prices that are contingent on the financing model.
Assume that all supply chains use trade credit financing. The incentive to deviate for the
supply chain, Gsp, is then defined as the producer surplus of the first deviating supply chain
(m = 1), minus the producer surplus when all firms use trade credit financing.
The left panel in Figure 3 shows the one time gain of deviation as a fraction of the one
period producer surplus under trade credit financing for different industry concentrations.
The relative payoff for deviation increases in the number of firms because producer surplus
declines faster than the payoff of deviation. The benefit of deviation is highest when both
states are equally likely as this case offers the highest benefit from charging state specific
marginal costs. Overall the one-time gain is relatively small staying below 9% in our exam-
ple. This one-time gain has to be seen in relation to the present value of any future losses
from the shift to a new product market equilibrium as well as against any transaction costs
that occur when moving from bank financing to trade credit financing.
To make collusion a sustainable equilibrium much of the literature (following (Green
19
and Porter 1984)) implements a punishment mechanism should a player deviate from the
collusive equilibrium. Most empirical evidence on punishment by other firms in an industry
is anecdotal and comes from competition authorities’ prosecutions of cartels. In response to
cheating by a cartel member, previous research funds episodes of outright price war eroding
almost all profits for a certain time as well as more measured and targeted punishments.
Citing police recorded phone conversations from a cartel prosecution against gas stations
in Quebec, (Clark and Houde 2014) document that over five consecutive weeks in 2005,
prices in Victoriaville were within 1 cent of the floor set by the government as a punishment
towards a dissident. (Porter 1983) documents price wars in response to suspected cheating
in an American railroad cartel, (De Roos 2006) discusses punishment price-wars in the
market for lysine. (Roux and Thoni 2015) examine targeted retaliation as a punishment
mechanism in cartels where cartel companies would enact specific measures to hit deviating
firms. One such targeted punishment is reported by (Harrington Jr et al. 2006) where in the
industrial and medical gases, cartel suppliers would set up ”hit lists” to target a deviator’s
consumers. (Genesove and Mullin 2001) document several cases in which deviating firms
in the American Sugar Cartel were punished by the other cartel members ”in degree and in
kind”.
We focus on a measured, ”in kind”, punishment strategy for which we assume that the
players commit to bank financing for a certain number of periods should one firm deviate
from the trade credit equilibrium. The right panel in Figure 3 illustrates the required length
of such a punishment phase to make deviation unprofitable. The present value of the losses
from collusion in the punishment phase decline in the discount rate, causing the required
length of the punishment phase to increase in r. Collusion from trade credit is most valuable
for medium concentrated industries (n=5) which therefore require a shorter punishment
phase. A required punishment phase of three to four periods documents at least in this
example that the gain from collusion through trade credit financing is large relative to the
short term benefit of a one time deviation.18
Another deterrent for deviation is potential switching costs. Abandoning vendor financ-
ing will in some industries impose significant costs on producers. In practice companies
create an institutional framework for vendor financing. For example, almost all car com-
panies have financing arms – separate corporations – that offer favorable financing for car
dealers’ inventory (floor plan financing). Set-up costs of these finance companies and long-
18In unreported results we find that under a ”price war” punishment strategy, where the producer surplus iscompeted away, one punishment period is enough to deter deviation for a wide range of parameter values. We alsofind that with a harsher punishment strategy trade credit can be maintained as collusive equilibrium even whenvery few firms refuse to participate in the cartel or for reasons outside of the model (e.g. legal restrictions) usebank financing.
20
term financing contracts with dealers make it very costly for car manufacturers to deviate
from the trade credit equilibrium for short term gain. For example, in the second quarter
of 2014, Ford Motor Credit Company received $424m or 19.8% of its financing revenue
from dealer financing and it had about 6300 employees. Shutting down such an institution
and laying off several thousand employees is costly, which will reduce or eliminate any
short-term gains from deviation. Setting up finance subsidiaries could therefore also serve
as a commitment device to the collusive trade credit equilibrium
5.2 Deviation by the retailer
Another possible deviation from the collusive equilibrium can be initiated by the retailer.
Since demand states are assumed to be observable but not contactable, the retailer can the-
oretically avoid paying the high trade credit interest rate by financing the unsold inventory
in the bad state with either cash or bank debt at the lower rate r and repaying the supplier
in full. The payment can be financed by hoarding cash or raising debt in our model. The
retailer is financially unconstrained, never defaults, and thus has always access to debt mar-
kets. However, while such a strategy would bring an immediate reward, the short-term gain,
as outlined above, has to be seen in relation to forgone long-term gains from collusion.19
In our model a deviation from the collusive equilibrium would be noted by both the
supplier and the competitors and the game would revert back to bank financing. Assuming
a similar punishment mechanism as above the retailer might not find it optimal to deviate
when the short-term gain from deviation is less than the present value of the forgone profits
during the punishment period. The left panel in Figure 4 shows the minimum required
length of the punishment period to deter deviation for different levels of the risk free rate,
r.20 Similarly to the findings of the previous section we find that a punishment of five
periods is sufficient to deter deviation for a wide range of parameter values.
For reasons outside of the model, holding cash might be associated with an opportunity
cost larger than the risk-free rate. One reason could be agency costs as managers extract
19The supplier can make the retailer indifferent with respect to the financing scheme with transfer payments. Carmanufacturers, for example, make ex-post transfer payments called ”holdbacks” to their retailers on a monthly orquarterly basis which are based on past sales volume. The IRS describes holdbacks in the following way: ’Whendealers acquire their new car inventory from manufacturers, usually the invoice includes a separately coded chargefor ”holdbacks.” Dealer holdbacks generally average two to three percent of the Manufacturer’s Suggested RetailPrice (MSRP) excluding destination and delivery charges. These amounts are returned to the dealer at a laterdate. The purpose of the ”holdbacks” is to assure the dealer of a marginal profit.’, see New Vehicle DealershipAudit Technique Guide 2004 - Chapter 14 - Other Auto Dealership Issues (12-2004), Internal Revenue Service.Suppliers can then refuse to pay holdbacks when retailers deviate to bank financing. Another potential transfermechanism is advertising which is often paid by the supplier and benefits the retailers’ sales.
20For the graph it is assumed that the opportunity cost of cash is the risk free rate r. All results are computednumerically.
21
0.02 0.04 0.06 0.08 0.101
2
3
4
5
6
0.2 0.4 0.6 0.8 1.0
0.05
0.10
0.15
Length
ofpunishmentperiod
Opportunitycost
ofcash
Risk free rate r Probability of good state q
n =3
n = 5
n = 10
Ab = 50
Ab = 60
Ab = 80
Figure 4. Deviation by the retailerLeft panel: minimum length of the punishment period, i.e. the number of periods that players must becommitted to play the bank financing equilibrium after a deviation by one retailer, to deter deviationsfrom the trade credit equilibrium. Right panel: the critical opportunity cost of cash holdings for whichholding cash is suboptimal. Unless otherwise specified the parameters for the graph are: Ag = 100, Ab =60, q = 1/2, r = 0.05.
private benefits from firms with excessive cash. (Pinkowitz, Stulz, and Williamson 2006)
document that corporate cash holdings are substantially discounted when investor protec-
tion is weak. A dollar inside the firm is valued at $0.91 in countries with above-median
investor protection and only worth $0.33 in other countries.21 (Duchin, Gilbert, Harford,
and Hrdlicka 2017) document that managers in poorly governed firms are more likely to
invest cash holdings into risky assets and in the process destroy shareholder value. An-
other reason might be that firms hold cash to invest in value creating projects without delay
when future access to capital markets is uncertain (see for example (Harford, Klasa, and
Maxwell 2014) or (Bates, Kahle, and Stulz 2009)). Diverting cash from its intended pur-
pose to refinance inventory creates an opportunity cost.
Assume that holding a dollar of cash costs rc per period as an opportunity cost. The
benefit of holding a dollar occurs only in the bad state, which happens with probability
(1 − q), and allows the retailer to save the trade credit interest rate cost rs on that dollar,
which would be due next period. The expected benefit of holding a dollar of cash is thus
(1 − q)rs/(1 + r) as long as the marginal good in the bad state is still financed with trade
credit. Once the whole leftover inventory in the bad state can be financed with cash the
marginal benefit of holding cash is zero. The right panel in Figure 4 plots the opportunity
cost rc for which the firm is indifferent with respect to holding cash or not. Firms are
21In a cross country comparison (Dittmar, Mahrt-Smith, and Servaes 2003) find that firms hold up to twice asmuch cash in countries with poor shareholder protection and that cash holdings are less correlated with typicalexplanatory variables. (Kalcheva and Lins 2007) show that in countries with weak shareholder protection firmvalues are lower when managers hold more cash.
22
eager to hold cash even when the opportunity cost is high whenever the difference between
choke prices is high (low Ab for given Ag) or when demand uncertainty is high (medium
q). When the good state gets realized very often (high q) holding cash is expensive as it will
rarely get deployed and thus firms only hold cash when the opportunity cost is low. The
trade credit interest rate converges to zero as the probability of the good state goes to zero
(see Proposition 2). With low trade credit penalties for holding cash, it is not advantageous
unless it is very cheap (low opportunity cost). Overall we notice that depending on the
opportunity cost associated with holding cash then the firm might find it optimal not to pay
off the supplier in the bad state.
5.3 Trade credit vs. classic collusion
Without any restrictions on their ability to collude, the supply chains can maximize their
profit if they coordinate their aggregate output to match that of an integrated monopolist.
We refer to the case where n supply chains equally split quantities and thus profits that
an integrated monopolist could obtain as classic collusion. In contrast, in our setting the
competitive Cournot outcome would be the bank financing case discussed above.22 In the
left panel of Figure 5 we compare the benefit of trade credit relative to bank financing and
classic collusion. We normalize a firm’s profit under classic collusion to one and the firm’s
profit under bank financing to zero. In the example in the left panel we can see that profit
under trade credit financing is in general lower than under classic collusion especially in
dispersed industries but can come close to the profit under classic collusion in concentrated
industries (three firms in this example).
Collusion through trade credit is also in many cases more stable than classic collusion.
We define the gain of deviation under classic collusion, Gcc, as the incremental profit that
a firm can obtain by optimizing its output decision given that all other players stick with
their output under classic collusion (see Appendix C). The right panel of Figure 5 shows
the region of the parameter space for which the gain of deviation from trade credit to bank
financing (Gsp as defined in Section 5.1) exceeds the gain from deviation in classic collu-
sion (Gcc). In other words, in this region collusion using trade credit is harder to maintain
than classic collusion. In our numerical analysis we only found such a region for a duopoly
when the good state is very unlikely and the bad state has very low demand. For industries
with more than two supply chains we found that under trade credit the incentive to deviate
is smaller than for classic collusion.
Trade credit as collusion mechanism also differs from classical collusion with respect to
the ease of coordination. (Levenstein and Suslow 2006) show that successful cartels invest
22(Lyandres, Fu, and Li 2016) follow a similar approach to examine collusion mechanisms in IPO pricing.
23
4 6 8 10
0.2
0.4
0.6
0.8
1.0
0.0 0.2 0.4 0.6 0.8 1.0
0
20
40
60
80
100
Relativeprofit
Chokeprice
inbadstate
Ab
number of firms n Probability of good state q
Classic collusion
Bank financing
Trade credit
n = 2
Figure 5. Stability of collusion with trade credit and classic collusionProfits under trade credit financing and bank financing relative to perfect collusion and a standardCournot oligopoly (left panel) and region of the parameter space for which deviation from trade creditfinancing to bank financing is more profitable relative to the deviation from a collusive oligopoly. Theparameters for the graph are, unless otherwise specified: Ag = 100, Ab = 60, q = 1/2, r = 0.05.
in monitoring capacity to ensure that cartel members stick to the collusive strategy. Under
the classical collusion, firms need to coordinate and enforce allocated output quantities as
each firm would find it profitable to deviate from their allocated quota. Output quantities
and prices are often unobservable and hence hard to police by cartel members. The trade
credit contract in our paper does not require any coordination except for the mutual agree-
ment to provide and use trade credit financing. Conditional on all firms in the industry using
trade credit to finance inventories, retailers and suppliers behave myopically and maximize
their profits, yet still achieve the collusive outcome.23
Another possibility to restrict competition is for the supplier to limit the amount she
sells to the retailer. In such an agreement it would again be optimal for the supply chain to
deviate and the points outlined in Section 5.1 would apply. We believe, however, that collu-
sion through trade credit is easier to maintain than collusion through supply restrictions. A
shift from trade credit financing to bank financing incurs transaction costs and is easier to
observe by competitors. Under classic collusion a deviation in the form of increased sales
to a retailer might be harder to observe. Furthermore, while restricting inventory levels
would restrict competition in the good state such a mechanism cannot make retailers more
aggressive in the bad state. Other, more elaborate schemes to achieve a collusive outcome
similar to the trade credit equilibrium might exist. However, our objective is not to derive
an optimal contract but to document that trade credit can lead to collusion in the product
23As stated in Equations (2) and (8) the retailer maximizes his expected profit for the bad state and for theoptimal choice of inventory, respectively. Similarly, the producer maximizes her profit given the chosen form offinancing as stated in Equations (9) and (10) for bank financing and trade credit financing, respectively.
24
market at the expense of the consumer.
5.4 Emergence of trade credit
While our model explores the benefits of trade credit financing over bank financing our
model like many other papers on collusion can only offer limited insights into the specific
mechanisms on how firms coordinate on the collusive equilibrium. We extend our model
to analyze the stability of the bank financing equilibrium in Appendix G. We extend the
baseline model such that one supply chain provides a small amount of trade credit to its
retailer while still mostly relying on bank financing while all other supply chains use pure
bank financing. When the amount of trade credit supplied is very small (less than the sales
in the bad state) then a penalty never materializes as the trade credit can always be repaid
within one period – even in the bad state. Therefore, the effect of trade credit financing on
the retailer’s product market behavior analyzed in the main body of the paper, is absent.
However, when the risk-free rate is positive, the deviating supply chain is better off by
providing a small amount of trade credit financing. Intuitively by providing trade credit the
supplier decreases the retailer’s funding costs for the marginal good, which incentivizes him
to hold a larger inventory and hence be more aggressive in the product market. Assuming
that the other supply chains stick with pure bank financing, the supply chain offering a bit
of trade credit financing can increase its producer surplus. Therefore pure bank financing
is inherently unstable and supply chains have an incentive to introduce trade credit.
5.5 Replicating the trade credit contract
Another issue to consider is why banks cannot offer a contract that replicates the trade
credit contract. The provision of trade credit is not a zero NPV project and can therefore
not be replicated easily by a competitive banking sector. If financing is profitable it will
be competed away by a competitive banking sector changing the financing rates and thus
product market competition. When pure financing has a negative NPV, banks will not offer
such a contract while a supplier can offset any financing losses with the gains in the product
market. Even if all obstacles could be overcome with a long-term contract that would
provide trade-credit- type financing, while breaking even on average for the banks, such a
contract would not have the same penalty rate and would thus have lower producer surplus.
In Appendix E we provide a detailed analysis with numerical examples and provide more
arguments why replication by outside financiers will not be easy to obtain.
25
6 Empirical evidence and extensions
6.1 Baseline evidence
We start with providing empirical evidence that trade credit use is inversely U-shaped in
industry concentration consistent with Proposition 4. For our analysis, we collect data on
US non-financial firms between 1980 and 2017 from Compustat and regress trade credit
use on industry concentration. We define trade credit usage as the logarithm of accounts
receivables over total sales24 and compute the Herfindahl Hirschmann index (HHI) based
on each firms share of total sales, where industry is defined based on 4-digit SIC codes.25
We include control variables commonly used in the literature: firm size is the logarithm
of sales, book leverage is book value of total liabilities over total assets, Cash/TA is the
amount of cash over total assets, market/book is the ratio of market value over book value
of equity, return on assets (ROA) is net income over total assets, tangibility is net property
plant and equipment over total assets, profit margin is sales minus costs of goods sold over
sales, free cash flow over total assets is defined as earnings before interest and taxes (EBIT)
minus taxes plus depreciation minus capital expenditures over total assets, acquisition is
a dummy equal to one if the company conducted an acquisition, and dividend paying is a
dummy indicating that the firm paid dividends. To control for outliers, we winsorize our
data at the 5% level for each variable.
For our analysis we run two regression specifications: first we regress trade credit use
on the HHI and on the squared HHI to capture the nonlinear relationship between trade
credit use and industry concentration. Second, we regress trade credit use on the HHI and
allow for a change in slope above the median by multiplying a dummy that equals one if
the HHI is above the median with the change in the HHI beyond the median. Formally, let
q50 be the median of the HHI distribution we estimate the following model
TC = a HHI + b 1HHI>q50(HHI− q50) + controls+ ε (11)
24While our model assumes that one supplier only contracts with one retailer, in practice one supplier mightdeliver goods to several retailers that serve different (potentially overlapping) markets, e.g. Ford and GM sellcars to several dealerships that serve a large city. The benefit of trade credit in our model is mainly driven bycompetition between suppliers, e.g. car producers. Therefore we use receivables of suppliers as a measure of tradecredit use. Trade credit use of retailers is harder to measure as many retailers are private and it might vary due tolocal competition in their markets.
25In unreported results we check for robustness by downloading the HHI of the largest 50 companies from theU.S. Economic Census for manufacturing companies. (Ali, Klasa, and Yeung 2009) point out that Compustatexcludes private companies which might lead to mismeasurement of industry concentration. Census concentrationdata is classified based on 4-digit SIC codes for the years 1982, 1987, and 1992, and uses the NAICS classificationfor the 1997, 2002, 2007, and 2012 censuses. We merge our datasets based on the respective industry classifica-tions. Industry concentration in years between censuses is set to the closest available census data point. We findthe basic results of our analysis confirmed for this smaller sample.
26
Table 2. Summary statistics of firm and industry dataMean Std.Dev. Median Min. Max.
Trade credit -2.048 0.752 -1.892 -4.213 -0.868HHI 0.260 0.192 0.210 0.011 1.000Firm Size 5.502 2.128 5.478 0.411 9.053Book Leverage 0.491 0.185 0.502 0.112 0.857Cash/TA 0.089 0.097 0.051 0.002 0.470Market/Book 2.205 1.628 1.724 0.447 10.618ROA 0.014 0.099 0.037 -0.512 0.153Tangible assets/TA 0.289 0.205 0.240 0.016 0.802Profit Margin 0.351 0.169 0.330 -0.031 0.792FCF/TA 0.021 0.074 0.037 -0.327 0.137Acquisition 0.400 0.490 0.000 0.000 1.000Dividend paying 0.457 0.498 0.000 0.000 1.000Trade credit use is defined as logarithm of receivables over total sales. HHI is the Herfindahl-Hirschman Index based on sales. Firm size is the logarithm of sales, book leverage is totalbook value of total liabilities over total assets, Cash/TA is the amount of cash over total assets,market/book is the ratio of market value over book value of equity, return on assets (ROA) is netincome over total assets, tangibility is net property plant and equipment over total assets, profitmargin is sales minus costs of goods sold over sales, free cash flow over total assets is defined asEBIT after taxes plus depreciation minus capital expenditures over total assets, acquisition is adummy equal to one if the company conducted an acquisition, and dividend paying is a dummyindicating that the firm paid dividends.
where 1HHI>q50 is an indicator function equal to one if HHI is above the median. In all our
regressions we control for time fixed effects to control for time variation in credit demand
through the business cycle and report clustered standard errors.26
Our baseline regression results are presented in Table 3. We confirm our prediction
of an inverse U-shaped use of trade credit over industry concentration for our sample of
U.S. firms. The results in Table 3 confirm a concave, quadratic relationship between trade
credit and industry concentration. For the piecewise linear regression specification, we
find that trade credit first increases in industry concentration and then drops once industry
concentration is high. Most control variables are of similar magnitude as in (Dass, Kale,
and Nanda 2014), who use a similar sample. Since the HHI is very stable it alone explains
26We do not include firm or industry fixed effects as they would pick up the variation in trade credit use acrossindustries that we seek to identify. A firm fixed effects model would essentially relate inter-temporal changes intrade credit use to inter-temporal changes in industry concentration. We refrained from using such a specificationbecause, first, we are not too sure how fast trade credit use will respond to changes in industry concentrationand, second, in many industries concentration does not change by much relative to possible measurement errorsin HHIs. We are concerned that most year-to-year changes in measured industry concentration are of a similarmagnitude than the ones resulting from new firms getting listed or other firms going private and thus entering orleaving the Compustat database.
27
little of the variation in overall trade credit use as indicated by its low R2. This effect could
be further attenuated due to imperfect controls (see (Oster 2019)). The goal of our paper
is not to find an important determinant of trade credit for all firms but to find evidence
consistent with the existence of trade credit as collusion mechanism.
6.2 Benefits of collusion and trade credit use
Our findings should be more pronounced if there is a greater ability or willingness by the
firms in an industry to sustain collusion. From a well developed literature in IO we know
that collusion in general is more sustainable when products are more homogenous, barriers
to entry exist, and demand is stable.27
To start we test if the inverse U-shape is more pronounced in industries with homoge-
nous products using the data of (Hoberg and Phillips 2010) and (Hoberg and Phillips 2016)
on product similarity. Based on text analysis of 10-K filings they measure how close two
companies’ products are and then construct an aggregate index on how similar competitors’
products are for each firm. Merging their data with ours reduces the size and length of or
sample.28
To check how the inverse U-shaped pattern of trade credit varies with similarity we run
the following regression model:
TC = a+ b1 HHI + b2 1Tercile1 HHI + b3 1Tercile3 HHI +
b4 HHI2 + b5 1Tercile1 HHI2 + b6 1Tercile3 HHI2 + controls+ ε (12)
where 1Tercile1 and 1Tercile3 are dummy variables set to one if the product similarity measure
is in the first and third tercile, respectively. Table 4 illustrates the results for the new sample.
In line with the idea that collusion is more beneficial when products are more homogeneous
we find that the inverse U-shape is only present when the firm’s competitors offer similar
products while the relation between trade credit use and HHI is not significant in industries
where companies are able to differentiate their products.29 We show all regressions with
and without control variables as some of the control variables such as, for example, ROA
could be an outcome of the collusive trade credit equilibrium.
Under our mechanism the collusion benefit of trade credit increases in demand volatil-
ity. Figure 6 plots the relative difference of the producer surplus of trade credit relative to
bank financing for different measures of demand volatility in our model. The left panel
27See surveys in e.g. (Scherer and Ross 1990), (Feuerstein 2005), or (Grout and Sonderegger 2005).28The merged data ranges from 1996-2017 while the original data spans a period from 1980-2017.29For simplicity we only present the specification with the squared HHI, the results of the piece wise regression
specification are available from the authors upon request.
28
Table 3. Regression results of trade credit use on market concentration.Number Obs. 93,901 93,901 93,901 93,901 93,901 93,901HHI2 -0.87*** -0.24** -0.22**
(0.1301) (0.0960) (0.0954)HHI 0.90*** 0.18* 0.20** 1.40*** 0.33** 0.36**
(0.1343) (0.0983) (0.0971) (0.2071) (0.1518) (0.1500)(HHI ≥ q50) -1.49*** -0.42** -0.42***× (HHI-q50) (0.2248) (0.1659) (0.1643)
Firm Size -0.06*** -0.05*** -0.06*** -0.04***(0.0027) (0.0027) (0.0027) (0.0027)
Book Leverage 0.06*** 0.05** 0.06*** 0.05**(0.0207) (0.0198) (0.0207) (0.0198)
Cash/TA -0.71*** -0.64*** -0.71*** -0.63***(0.0342) (0.0348) (0.0343) (0.0346)
Market/Book -0.01*** -0.01*** -0.01*** -0.01***(0.0022) (0.0021) (0.0022) (0.0021)
ROA 0.10** 0.04 0.09** 0.03(0.0453) (0.0428) (0.0456) (0.0429)
Tangible assets/TA -1.09*** -1.11*** -1.08*** -1.10***(0.0343) (0.0342) (0.0331) (0.0329)
Profit Margin 0.69*** 0.72*** 0.69*** 0.72***(0.0281) (0.0279) (0.0286) (0.0284)
FCF/TA -0.35*** -0.35*** -0.35*** -0.36***(0.0690) (0.0667) (0.0689) (0.0666)
Acquisition 0.16*** 0.16*** 0.16*** 0.16***(0.0070) (0.0070) (0.0070) (0.0070)
Dividend paying 0.07*** 0.07*** 0.07*** 0.07***(0.0084) (0.0077) (0.0084) (0.0077)
R2 0.0139 0.1474 0.1538 0.0168 0.1477 0.1541Year fixed effects Yes No Yes Yes No YesThe dependent variable is trade credit use, which is defined as logarithm of receivables overtotal sales, HHI is the Herfindahl-Hirschman Index based on sales. The control variables aredefined as in Table 2. One, two, and three stars indicate significance at the 10%, 5%, and 1%level, respectively.
29
Table 4. Regression results of trade credit use on market concentration.Number of Obs. 68,282 68,282 68,282 45,520 68,282HHI2 * T1 similarity 0.53 *** 0.13 -0.08
(0.1311) (0.1180) (0.1120)HHI2 -0.93 *** -0.48 *** -0.06 0.05 0.12
(0.1419) (0.1292) (0.1102) (0.0830) (0.1187)HHI2 * T3 similiarity -1.47 *** -0.63 ** -0.74 *** -0.58 **
(0.3336) (0.2657) (0.2752) (0.2705)HHI * T1 similiarity -0.52 *** -0.11 0.02
(0.1259) (0.1128) (0.1109)HHI 0.96 *** 0.41 *** 0.02 -0.07 -0.10
(0.1477) (0.1292) (0.1087) (0.0842) (0.1140)HHI * T3 similiarity 1.38 *** 0.45 ** 0.54 ** 0.42 *
(0.2805) (0.2184) (0.2293) (0.2221)T1 similiarity 0.20 *** 0.06 *** 0.05 **
(0.0241) (0.0215) (0.0216)T3 similiarity -0.25 *** -0.11 *** -0.17 *** -0.10 ***
(0.0463) (0.0355) (0.0380) (0.0362)Firm Size -0.05 *** -0.05 *** -0.06 ***
(0.0030) (0.0037) (0.0030)Book Leverage 0.02 0.09 *** 0.05 **
(0.0227) (0.0279) (0.0232)Cash/TA -0.61 *** -0.49 *** -0.73 ***
(0.0386) (0.0452) (0.0378)Market/Book -0.01 *** -0.01 *** -0.01 **
(0.0024) (0.0028) (0.0025)ROA 0.00 -0.05 0.11 **
(0.0477) (0.0558) (0.0480)Tangible assets/TA -1.08 *** -1.09 *** -1.07 ***
(0.0381) (0.0455) (0.0384)Profit Margin 0.70 *** 0.77 *** 0.66 ***
(0.0323) (0.0387) (0.0324)FCF/TA -0.33 *** -0.43 *** -0.34 ***
(0.0709) (0.0834) (0.0729)Acquisition 0.17 *** 0.18 *** 0.17 ***
(0.0078) (0.0097) (0.0078)Dividend paying 0.05 *** 0.06 *** 0.07 ***
(0.0084) (0.0099) (0.0091)R2 0.0150 0.0270 0.1671 0.1848 0.1600Year fixed effects Yes Yes Yes Yes NoTerciles in Similiarity all all all 1 and 3 allThe dependent variable is trade credit use, which is defined as logarithm of receivables overtotal sales, HHI is the Herfindahl–Hirschman Index based on Compustat data. The controlvariables are defined as in Table 2. The T1 and T3 dummies are one for firms in the bottom andtop terciles of firms’ product similarity measure from Hoberg and Phillips (2010), respectively.One, two, and three stars indicate significance at the 10%, 5%, and 1% level, respectively.
30
100 120 140 160 180 200
0.04
0.06
0.08
0.10
0.12
0.2 0.4 0.6 0.8
0.005
0.010
0.015
Relativebenefitoftradecredit
Relativebenefitoftradecredit
Dispersion good - bad state Probability of good state q
number of firm
s n = 3
n = 5
n = 7
n = 3
n = 5
n = 7
Figure 6. Relative difference in producer surplus of trade credit relative to bank financing fordifferent measures of demand volatility.The relative benefit of trade credit financing as a function of the absolute difference between the goodand the bad demand states keeping the choke price in the bad state fixed (left panel), and as a functionof the probability of the good state q. The parameters for the graph are, unless otherwise specified:Ag = 100, Ab = 60, q = 1/2, r = 0.05.
shows that trade credit is more beneficial as the difference in choke prices, Ag − Ab,
increases. Intuitively higher demand volatility increases the benefit of state contingent
marginal costs that is achieved by trade credit. The right panel shows by means of an ex-
ample that the benefit of trade credit is increasing in uncertainty about the demand state,
i.e. when the good and the bad state are of similar likelihood (q near 1/2).
To test this prediction empirically we measure the volatility of changes in aggregate
sales per industry over the last three years. Table 5 documents that the inverse U-shape
of trade credit use in industry concentration can only be found in volatile industries and is
not present in industries with stable demand. While being no causal proof, the evidence
is consistent with the idea that trade credit is more valuable as a collusion mechanism in
industries with more demand uncertainty.
We also examine other suggestions that are summarized in (Grout and Sonderegger
2005). As they point out, collusion is more sustainable in stable or shrinking industries. In
growing industries gains from obtaining a higher market share by deviating are more likely
to outweigh the benefits of collusion. In our framework we would therefore expect to see a
more pronounced hump-shape in stable or declining industries. In line with our prediction
Table 6 documents that the inverse U-shape relation between trade credit use and industry
concentration is only present in the low tercile of past industry demand growth.
Collusion is also more sustainable when barriers to entry are high. Incumbent firms can
enjoy oligopoly rents as long as entry of new firms, who could compete away a substantial
part of these rents, is unlikely. One commonly used measure of barriers to entry is the ratio
of tangible assets to total assets. Table 7 presents our results for different asset tangibility.
31
Table 5. Regression results of trade credit use on market concentration for different halves of demandvolatility.Number of Obs. 87,169 87,169 87,169 87,169HHI2 -0.87 *** -0.49 ** 0.05 0.03
(0.1383) (0.1955) (0.1425) (0.1468)HHI2 * High Volatility -0.76 *** -0.49 ** -0.47 **
(0.2700) (0.2156) (0.2163)HHI 0.89 *** 0.57 *** -0.01 -0.01
(0.1409) (0.1976) (0.1415) (0.1467)HHI * High Volatility 0.66 ** 0.36 * 0.33
(0.2770) (0.2200) (0.2205)High Volatility -0.13 ** -0.04 -0.03
(0.0560) (0.0444) (0.0442)Firm Size -0.05 *** -0.06 ***
(0.0028) (0.0027)Book Leverage 0.05 *** 0.07 ***
(0.0204) (0.0210)Cash/TA -0.61 *** -0.69 ***
(0.0351) (0.0350)Market/Book -0.01 *** -0.01 ***
(0.0022) (0.0023)ROA -0.01 0.07
(0.0419) (0.0443)Tangible assets/TA -1.10 *** -1.09 ***
(0.0357) (0.0358)Profit Margin 0.71 *** 0.68 ***
(0.0288) (0.0290)FCF/TA -0.24 *** -0.24 ***
(0.0652) (0.0679)Acquisition 0.16 *** 0.16 ***
(0.0073) (0.0073)Dividend paying 0.07 *** 0.08 ***
(0.0080) (0.0085)Year FE yes yes yes noR2 0.0129 0.0145 0.1532 0.1476Demand volatility is estimated as standard deviation of industry wide sales in three years pre-ceding the observation year. The control variables are defined as in Table 2. The high volatilitydummy is equal to one for the upper half of the volatility distribution. One, two, and three starsindicate significance at the 10%, 5%, and 1% level, respectively.
32
Table 6. Regression results of trade credit use on market concentration comparing the highest and thelowest tercile of past demand growth.Number of Obs. 59,397 59,397 59,397 59,397HHI2 -0.66 *** -0.09 0.25 0.29
(0.1614) (0.2538) (0.1853) (0.1878)HHI2 * T1 growth -1.13 *** -0.55 ** -0.61 **
(0.3193) (0.2564) (0.2554)HHI 0.66 *** -0.01 -0.37 ** -0.44 **
(0.1650) (0.2479) (0.1791) (0.1825)HHI * T1 growth 1.32 *** 0.64 ** 0.71 ***
(0.3220) (0.2591) (0.2587)T1 growth -0.23 *** -0.08 -0.12 **
(0.0643) (0.0526) (0.0519)Firm Size -0.05 *** -0.06 ***
(0.0033) (0.0035)Book Leverage 0.05 ** 0.06 ***
(0.0241) (0.0247)Cash/TA -0.69 *** -0.77 ***
(0.0432) (0.0435)Market/Book -0.01 *** -0.01 ***
(0.0026) (0.0027)ROA 0.00 0.06
(0.0525) (0.0566)Tangible assets/TA -1.07 *** -1.07 ***
(0.0411) (0.0416)Profit Margin 0.68 *** 0.65 ***
(0.0346) (0.0352)FCF/TA -0.25 *** -0.26 ***
(0.0793) (0.0819)Acquisition 0.16 *** 0.16 ***
(0.0087) (0.0087)Dividend paying 0.07 *** 0.07 ***
(0.0095) (0.0100)Year FE yes yes yes noR2 0.0145 0.0185 0.1496 0.1440Demand growth is measured over the last three years of industry wide sales. The control vari-ables are defined as in Table 2. The T1 growth-dummy is set to one for firms in the lower tercileof demand growth. One, two, and three stars indicate significance at the 10%, 5%, and 1%level, respectively.
33
In line with our prediction we observe that the inverse U-shape is most pronounced when
asset tangibility is high.
In their paper, (Grout and Sonderegger 2005) predict the likelihood of a cartel for each
industry in their sample based on Rev 1.1 on the European NACE industry classification.
We take the 37 industries with the highest probability of having a cartel of Table 4.4 in their
paper and translate them to NAICS codes using the mapping table from the US Census
Bureau website.30 Label firms in these 37 NACE industries as cartel firms. Cartel firms
and non-cartel firms in our sample have comparable distributions of industry concentration
with a mean HHI of 0.219 and 0.259 and a HHI standard deviation of 0.180 and 0.194 for
cartel and con cartel firms, respectively. To check whether the inverse U-shaped pattern of
trade credit use and industry concentration coincides with evidence of collusion we run the
following regression model:
TC = a+ b1 HHI + b2 HHI2 + b3 1Cartel HHI + b4 1Cartel HHI2 + controls+ ε (13)
where 1Cartel is a dummy variable set to one if an industry has a high likelihood of being in
a cartel .
Table 8 summarizes our findings from estimating the model in Equation (13) as well as
some simplified specifications. With control variables the inverse U-shape is only signifi-
cant for industries that (Grout and Sonderegger 2005) identify as likely to have a cartel.
6.3 Relative bargaining power of downstream industries
One important assumption of our baseline model is that suppliers can unilaterally set the
price and the trade credit interest rate. In reality, large retailers such as Walmart, have
substantial bargaining power and might therefore extract terms that are substantially better
than what the supplier wants to charge. Bargaining over price and over the trade credit
interest rate has a similar effect in our model. We start with negotiations over the wholesale
price. While bargaining for a lower price might be optimal for a myopic retailer, it is not
beneficial overall, in our model, for the industry. A lower purchase price for the retailer will
not automatically translate in a higher producer surplus as competition in the retail market
will intensify and retail prices will drop.
To explore this idea, we extend our model to incorporate a simple bargaining game
between the supplier and a myopic retailer. Assume that just before the retailer places the
order with the supplier, they engage in a bilateral Nash bargaining game over the price
30Available at https://www.census.gov/eos/www/naics/concordances/2002 NAICS to NACE Rev. 1.1.xls. Wemap the tree digit NACE codes from (Grout and Sonderegger 2005) into 6-digit NAICS codes allowing for arelative precise matching.
34
Table 7. Regression results of trade credit use on market concentration for different tangible assets.Number of Obs. 93,901 93,901 93,901 93,901HHI2 -0.87 *** 0.18 * -0.02 -0.02
(0.1301) (0.1028) (0.0870) (0.0938)HHI2 * High Tangibility -1.27 *** -0.43 *** -0.47 ***
(0.1846) (0.1572) (0.1598)HHI 0.90 *** -0.20 * 0.02 -0.01
(0.1343) (0.1010) (0.0836) (0.0919)HHI * High Tangibility 1.32 *** 0.38 ** 0.43 ***
(0.1892) (0.1587) (0.1614)High Tangibility -0.62 *** -0.14 *** -0.14 ***
(0.0383) (0.0288) (0.0295)Firm Size -0.04 *** -0.06 ***
(0.0027) (0.0027)Book Leverage 0.05 ** 0.06 ***
(0.0200) (0.0208)Cash/TA -0.64 *** -0.72 ***
(0.0347) (0.0340)Market/Book -0.01 *** -0.01 ***
(0.0021) (0.0022)ROA 0.04 0.10 **
(0.0425) (0.0451)Tangible assets/TA -0.93 *** -0.93 ***
(0.0444) (0.0450)Profit Margin 0.71 *** 0.68 ***
(0.0277) (0.0279)FCF/TA -0.35 *** -0.34 ***
(0.0663) (0.0688)Acquisition 0.16 *** 0.16 ***
(0.0069) (0.0070)Dividend paying 0.07 *** 0.08 ***
(0.0078) (0.0084)Year FE yes yes yes noR2 0.0135 0.0893 0.1545 0.1485The control variables are defined as in Table 2. The High Tangibility-dummy is set to onefor firms in the upper half of the tangibility distribution. One, two, and three stars indicatesignificance at the 10%, 5%, and 1% level, respectively.
35
Table 8. Trade Credit use and likelihood of being in a cartelNumber of Obs. 93,901 93,901 93,901 91,130HHI2 -0.87 *** -0.58 *** 0.03 0.00
(0.1301) (0.1305) (0.0957) (0.0962)HHI 0.90 *** 0.64 *** -0.03 -0.04
(0.1343) (0.1317) (0.0953) (0.0964)1Cartel HHI2 -1.12 *** -0.93 *** -0.89 ***
(0.1078) (0.0836) (0.0840)1Cartel HHI 1.08 *** 0.94 *** 0.92 ***
(0.0749) (0.0561) (0.0571)Firm Size -0.04 *** -0.05 ***
(0.0026) (0.0026)Book Leverage 0.05 ** 0.06 ***
(0.0197) (0.0206)Cash/TA -0.64 *** -0.72 ***
(0.0344) (0.0339)Market/Book -0.01 *** -0.01 ***
(0.0021) (0.0022)ROA 0.05 0.11 **
(0.0424) (0.0448)Tangible assets/TA -1.11 *** -1.10 ***
(0.0335) (0.0337)Profit Margin 0.69 *** 0.66 ***
(0.0272) (0.0274)FCF/TA -0.36 *** -0.36 ***
(0.0654) (0.0678)Acquisition 0.16 *** 0.16 ***
(0.0069) (0.0069)Dividend paying 0.06 *** 0.07 ***
(0.0076) (0.0083)Year FE yes yes yes noR2 0.0139 0.0249 0.1626 0.1560Trade credit use and market concentration with an interaction dummy of firms that are likelyto be in a cartel as predicted by the analysis of Grout and Sonderegger (2005). The controlvariables are defined as in Table 2. One, two, and three stars indicate significance at the 10%,5%, and 1% level, respectively.
36
0.2 0.4 0.6 0.8 1.0
1
2
3
4
5
0.2 0.4 0.6 0.8 1.0
1
2
3
4
5
BenefitofTradeCredit
BenefitofTradeCredit
Bargaining power of retailer Bargaining power of retailer
number of firms n = 3n = 5
n = 7 q = 1/4
q = 1/2
q =3/4
Figure 7. Benefit of trade credit defined as the producer surplus under trade credit financing minusthe producer surplus under bank financing as a function of the retailers’ bargaining power. Theparameters for the graph are, unless otherwise specified: Ag = 100, Ab = 50, q = 1/2, r = 0.05, n = 3.
P where the retailer is assumed to have a relative bargaining power of γ ∈ [0, 1]. If the
retailer has all the bargaining power, he will offer the reservation price of the supplier which
is the marginal cost of producing the good that we set to zero in our model. When all the
bargaining power is with the supplier, as it is the case in the basic model of the paper, she
sets the price to, PB and P T , as derived in Propositions 1 and 2 for bank financing and
trade credit, respectively. Assume that the supplier and the retailer settle for a γ-weighted
average price between those two values, γPB and γP T , for bank and trade credit financing,
respectively.31
Figure 7 shows the benefit of trade credit defined as the producer surplus under trade
credit financing minus the producer surplus under bank financing as a function of γ. When
retailers have all the bargaining power and drive the price of the good in the wholesale
market to zero, no financing is needed and the form of financing has no impact on the
outcome in the product market. When the supplier has all the bargaining power, we obtain
the result of the basic model in the paper that trade credit can work as collusion mechanism.
We find a similar effect when we extend the model to allow for bargaining over the trade
credit interest rate rs. The benefit of trade credit over bank financing decreases in the
retailer’s bargaining power. When the retailer can extract a lower rate, the marginal cost
difference between states diminishes and the retailer’s optimal sales become less sensitive
to the demand state similar to the bank financing equilibrium.
Our model predicts that trade credit is less useful as a collusion mechanism when the
bargaining power of the retailer is high. Empirically we use downstream industry concen-
31We take this approach to provide some intuition and rely on many limiting assumptions. Amongst othersthe retailer is assumed to be myopic and does not take the actions of other retailers into account, all retailersare assumed to have the same bargaining power, suppliers are assumed to all have zero production cost, and thebargaining is modeled as a standalone game. We rule out any dynamic, path dependent, and other more complexbargaining strategies.
37
tration as a proxy for the retailers relative bargaining power. We start with identifying the
downstream industries based on the Bureau of Economic Analysis (BEA) make-use tables,
which contain data on 71 industries. We map to 54 downstream industries in our sample
as some industry classifications in the BEA tables relate to different branches of govern-
ment or industries, which are not in our sample. We then find for each industry the fraction
of its output used in the downstream industries and compute the downstream HHI as the
weighted average of the downstream industries’ HHIs. Table 9 shows the results for the
overall sample and with the inclusion of the downstream HHI as a control variable. While
the downstream HHI itself is insignificant as a control variable (column 3), we get inter-
esting results from including dummies for terciles of downstream industry concentration
in a specification similar to Equation (12). The inverse U-shape is more pronounced the
lower the downstream industry concentration is. When downstream industry concentration
is high the inverse U-shape is significantly less pronounced which is consistent with the
idea that firms in a more concentrated downstream industry have more bargaining power
and thus make trade credit as a collusion mechanism less attractive.
As a second way to control for downstream industry concentration we use fuzzy text-
matching as well as manual matching to identify the names of each firm’s largest customers
in the segment data of the Compustat database. Our sample size is dramatically reduced
as we lose 30 years of data (segment data starts in 2009) and because we cannot match
some customers to firms in the Compustat database. We then compute the average HHI for
all downstream firms as simple average because sales data to individual customers is not
always available and we do not want to lose any more observations. Table 10 summarizes
our findings. For this sample the downstream HHI is significant as a control variable (col-
umn 4) indicating that higher downstream industry concentration corresponds to less use
of trade credit, and the significance of the hump shape disappears for the whole sample.
Partitioning the sample according to the downstream HHI however, again reveals that even
in this drastically reduced sample the inverse U-shape is present when downstream industry
concentration is low.
6.4 Cash holdings and trade credit
Based on the discussion in Section 5.2 we would expect that trade credit is less useful as a
collusion mechanism in industries that for some reason outside of the model have high cash
holdings. To take this idea to the data we compute the average annual industry cash holdings
by computing total cash held by firms in an industry in a year over total assets in an industry
and repeat our main analysis for different subsamples based on the average industry cash
holdings. Table 11 presents our findings. In line with the intuition that incentives to deviate
38
Table 9. Trade credit use and market concentration controlling for downstream industry concentration,which is measured as the weighted average HHI of downstream industries according to the BEA make-use tables.Number of Obs. 73,574 73,574 73,574 73,574 73,574 73,574HHI2 * T1 dstr HHI -2.40*** -1.42*** -1.35***
(0.4011) (0.2748) (0.2857)HHI2 -1.19*** -0.64*** -0.64*** -0.36*** -0.28*** -0.31***
(0.1561) (0.1039) (0.0931) (0.1238) (0.0985) (0.1023)HHI2 * T3 dstr HHI 0.60*** 0.52*** 0.51***
(0.1653) (0.1351) (0.1431)HHI * T1 dstr HHI 2.23*** 1.36*** 1.29***
(0.4058) (0.2751) (0.2866)HHI 1.21*** 0.59*** 0.59*** 0.48*** 0.23*** 0.24**
(0.1632) (0.1070) (0.0933) (0.1148) (0.0892) (0.0939)HHI * T3 dstr HHI -0.85*** -0.55*** -0.55***
(0.1630) (0.1315) (0.1422)T1 dstr HHI -0.47*** -0.30*** -0.31***
(0.0752) (0.0517) (0.0526)T3 dstr HHI 0.11*** 0.03 0.00
(0.0337) (0.0266) (0.0285)Dstr HHI 0.00
(0.0734)Firm Size -0.03*** -0.03*** -0.03*** -0.04***
(0.0029) (0.0029) (0.0028) (0.0029)Book Leverage 0.06*** 0.06*** 0.09*** 0.11***
(0.0209) (0.0211) (0.0211) (0.0221)Cash/TA -0.64*** -0.64*** -0.61*** -0.70***
(0.0357) (0.0356) (0.0353) (0.0343)Market/Book -0.01*** -0.01*** -0.01*** -0.01***
(0.0022) (0.0022) (0.0022) (0.0023)ROA 0.17*** 0.17*** 0.18*** 0.26***
(0.0440) (0.0438) (0.0437) (0.0461)Tangible assets/TA -1.33*** -1.33*** -1.29*** -1.28***
(0.0407) (0.0400) (0.0380) (0.0385)Profit Margin 0.77*** 0.77*** 0.76*** 0.73***
(0.0315) (0.0322) (0.0321) (0.0324)FCF/TA -0.54*** -0.54*** -0.58*** -0.58***
(0.0676) (0.0675) (0.0674) (0.0701)Acquisition 0.12*** 0.12*** 0.12*** 0.11***
(0.0069) (0.0069) (0.0068) (0.0068)Dividend paying 0.02** 0.02** 0.02*** 0.03***
(0.0075) (0.0074) (0.0075) (0.0082)Year FE yes yes yes yes yes noR2 0.0204 0.2146 0.2146 0.0438 0.2239 0.2172The control variables are defined as in Table 2. The T1 dstr HII and T3 dstr HHI-dummiesare set to one for firms in the lower and upper tercile of the downstream HHI distribution,respectively. One, two, and three stars indicate significance at the 10%, 5%, and 1% level,respectively.
39
Table 10. Trade credit use and market concentration controlling for downstream industry concentrationmeasured using information on large customers from the Compustat segment data.Number of Observations 1,794 1,794 1,794 1,794 1,794 1,794HHI2 * T1 dstr HHI -2.34*** -1.53** -1.43**
(0.6708) (0.6097) (0.6000)HHI2 0.11 -0.11 -0.25 0.59 0.11 0.03
(0.2748) (0.2401) (0.2363) (0.4778) (0.4381) (0.4377)HHI2 * T3 dstr HHI 0.39 0.12 0.24
(0.5446) (0.4984) (0.5082)HHI * T1 dstr HHI 2.11*** 1.13** 1.03*
(0.6465) (0.5758) (0.5727)HHI -0.14 0.05 0.22 -0.42 0.05 0.11
(0.2845) (0.2500) (0.2423) (0.4644) (0.4106) (0.4150)HHI * T3 dstr HHI -0.60 -0.24 -0.35
(0.5512) (0.4976) (0.5143)T1 dstr HHI -0.25** 0.00 0.01
(0.1118) (0.0963) (0.0970)T3 dstr HHI 0.01 -0.07 -0.04
(0.1062) (0.0927) (0.0975)Dstr HHI -0.39***
(0.0703)Firm Size -0.02* -0.03** -0.03* -0.02*
(0.0141) (0.0134) (0.0134) (0.0136)Book Leverage 0.26** 0.29*** 0.29*** 0.28***
(0.1018) (0.0980) (0.0976) (0.0986)Cash/TA -0.05 -0.13 -0.17 -0.19
(0.1741) (0.1731) (0.1731) (0.1771)Market/Book -0.08*** -0.08*** -0.08*** -0.07***
(0.0133) (0.0130) (0.0127) (0.0132)ROA 0.22 0.26 0.20 0.25
(0.2541) (0.2461) (0.2460) (0.2478)Tangible assets/TA -0.46*** -0.62*** -0.61*** -0.63***
(0.1297) (0.1325) (0.1368) (0.1373)Profit Margin 0.67*** 0.64*** 0.67*** 0.65***
(0.1367) (0.1344) (0.1295) (0.1337)FCF/TA -0.40 -0.41 -0.28 -0.45
(0.3895) (0.3735) (0.3661) (0.3558)Acquisition -0.01 -0.02 -0.02 -0.02
(0.0331) (0.0319) (0.0323) (0.0328)Dividend paying -0.09*** -0.09*** -0.09*** -0.08**
(0.0338) (0.0324) (0.0316) (0.0317)Year FE yes yes yes yes yes noR2 0.0042 0.1519 0.1791 0.0382 0.1875 0.1751The control variables are defined as in Table 2. The T1 dstr HII and T3 dstr HHI-dummiesare set to one for firms in the lower and upper tercile of the downstream HHI distribution,respectively. One, two, and three stars indicate significance at the 10%, 5%, and 1% level,respectively.
40
are higher when cash is readily available, we find that our inverse U-shaped relationship
between trade credit and industry concentration is only significant for forms that are in the
lower half of the cash holdings distribution.
Another potential mechanism for a supply chain to deviate from the collusive equi-
librium is to re-allocate inventory. Suppose, for example, that one producer supplies two
retailers in segmented markets. When demand in one market is low and is high in the other
market the supplier could re-allocate inventory to avoid penalties and inventory restrictions.
Another possibility to deviate can be by speeding up production. If the supplier could in-
stantaneously create new goods and ship them to the retailer without delay when demand is
high, the supply chain can generate a one-time extra payoff by deviating from the equilib-
rium. Similar to the argument above with cash buffers and the discussion in Section 5 each
supply chain has to balance the short-term gain from deviation with the long-term benefit
of collusion. If a supplier, for some exogenous reason related to the industry has to hold
larger inventories it might be harder to sustain the collusive equilibrium. Consistent with
this idea we find in unreported results that the inverse-u shape between trade credit use and
industry concentration is more pronounced when supplier-inventory levels are low.
7 Conclusion
We investigate how different kinds of debt affect output market equilibrium by comparing
bank and trade credit financing, and offer a novel explanation that why trade credit exists
even though it is often viewed as an expensive financing option. We argue that trade credit
financing modifies a retailer’s ex-ante inventory policy and ex-post product market strat-
egy, respectively, in an uncertain demand environment. When demand is low the retailer
sells more to avoid financing the unsold inventory at the high trade credit rate ex-ante the
possibility of having to pay the high trade credit interest rate induces the retailer to reduce
his optimal inventory level, which in turn limits competition in the product market when
demand is high.
The distortions that trade credit financing introduces to product markets allows produc-
ers to increase their profits at the expense of consumer surplus. We can therefore see trade
credit as a collusion mechanism between supply chains that mitigates competition. We of-
fer a novel explanation why financially unconstrained firms finance their inventories with
expensive trade credit and why suppliers are able to offer a financing contract that cannot
be replicated by banks.
Our findings also have important policy implications for industries that rely heavily
on vendor financing, often through institutionalized finance companies, such as the auto-
41
Table 11. Trade credit use and market concentration for different levels of industry cash holdings.Number of Observations 81,389 81,389 81,389 81,389HHI2 -0.95 *** -0.59 *** -0.07 -0.07
(0.1314) (0.0997) (0.0854) (0.0858)HHI2 * Low Cash -0.88 *** -0.30 ** -0.29 **
(0.1791) (0.1472) (0.1475)HHI 1.00 *** 0.63 *** 0.04 0.00
(0.1363) (0.1040) (0.0881) (0.0888)HHI * Low Cash 0.87 *** 0.28 ** 0.30 **
(0.1676) (0.1382) (0.1381)Low Cash -0.07 ** -0.08 *** -0.09 ***
(0.0309) (0.0267) (0.0261)Firm Size -0.05 *** -0.06 ***
(0.0035) (0.0033)Book Leverage 0.07 *** 0.08 ***
(0.0215) (0.0222)Cash/TA -0.82 *** -0.94 ***
(0.0743) (0.0698)Market/Book -0.01 *** -0.01 ***
(0.0024) (0.0025)ROA 0.02 0.06
(0.0472) (0.0503)Tangible assets/TA -1.06 *** -1.04 ***
(0.0334) (0.0336)Profit Margin 0.74 *** 0.71 ***
(0.0303) (0.0304)FCF/TA -0.32 *** -0.31 ***
(0.0713) (0.0737)Acquisition 0.16 *** 0.16 ***
(0.0073) (0.0074)Dividend paying 0.08 *** 0.08 ***
(0.0083) (0.0089)Year FE yes yes yes noR2 0.0158 0.0190 0.1537 0.1477The control variables are defined as in Table 2. The Low Cash-dummy is set to one for firmsin the lower half of the industry cash holdings distribution. One, two, and three stars indicatesignificance at the 10%, 5%, and 1% level, respectively.
42
mobile industry. All major car producers own finance companies that provide financing
of their retailers’ inventories, often referred to as floorplan financing. Our analysis shows
that allowing commercial firms to engage in financing activities can reduce competition.
Our paper also contributes to the long ongoing discussion in the U.S. on the separation of
banking and commerce. The recent Dodd-Frank enacted a three-year moratorium on the
creation of industrial loan companies (ILCs) in the U.S., which are often owned by large
industrial producers and provide financing to the firms clients. Our analysis provides an
argument that separation of banking and commerce can help in shutting down a potential
collusion mechanism amongst producers.
43
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A Proofs.
Proof of Proposition 1:
There exists a subgame perfect Nash equilibrium under bank financing such Proof.According to Equation (2), the first order condition to solve QBb is
∂
∂QBb
[(Ab −QBb −Q
−i,Bb )QBb − CBb
]= 0 (14)
Solving the partial derivative and substituting the cost CBg , Equation (14) becomes
Ab − 2QBb −Q−i,Bb + PB = 0 (15)
which yields the best response function
QBb =Ab −Q−i,B
b + PB
2(16)
Assuming that all firms are symmetric we setQ−i,Bb = (n−1)QBb and solve for the optimal
quantity that the retailer offers in the bad state which is
QBb =Ab − PB
n+ 1(17)
According to Equation (8), the first order condition to solve QBb is
∂
∂QBg
[(1− q)ωBb + qωBg
]= 0 (18)
By substituting the cost CBg and the optimal quantity that the retailer offers in the bad
state, QBb , and solving the partial derivative, Equation (18) becomes
Ag − 2QBg −Q−i,Bg + PB = 0 (19)
which yields the best response function
QBg =Ag −Q−i,B
b + PB
2(20)
Assuming that all firms are symmetric, we setQ−i,Bg = (n−1)QBg and solve for the optimal
quantity that the retailer offers in the good state which is
QBg =Ag − PB
n+ 1(21)
49
According to Equation (9), the first order condition to solve PB is:
∂
∂PB[(1 + r)PBQBg − (1− q)PB(QBg −QBb ))
]= 0 (22)
By substituting the optimal quantities, QBb , QBg , that the retailer offers in a bad state
and a good state, respectively, and solving the partial derivative, Equation (22) becomes
Agq +Ab(1− q)− 2PB
n+ 1= 0 (23)
which yields the price charged by a supplier under bank financing,
PB =2
n+ 3[Agq +Ab(1− q)] (24)
By substituting the equilibrium price into the Equation (17) and Equation (21), the
quantities sold in the good state and the bad state are (3+n−2q)Ag−2(1−q)Ab(n+3)(n+1) and 2qAg+(1+n+2q)Ab
(n+3)(n+1) ,
respectively.
Proof of Proposition 2Proof. According to Equation (2), the first order condition to solve QTb is:
∂
∂QTb
[(Ab −QTb −Q
−i,Tb )QTb − CTb
]= 0 (25)
Solving the partial derivative and substituting the cost CTb , Equation (25) becomes:
Ab − 2QTb −Q−i,Tb + P T (1− rs) = 0 (26)
which yields the best response function
QTb =Ab −Q−i,T
b + P T (1− rs)2
(27)
Assuming that all firms are symmetric we setQ−i,Tb = (n−1)QTb and solve for the optimal
quantity that the retailer offers in the bad state which is
QTb =Ab − P T (1− rs)
n+ 1(28)
According to Equation (8), the first order condition to solve QTb is
∂
∂QTg
[(1− q)ωTb + qωTg
]= 0 (29)
50
By substituting the cost CTg and the optimal quantity that the retailer offers in the bad
state, QTb , and solving the partial derivative, Equation (29) becomes
q(Ag − 2QTg −Q−i,Tg − P T )− (1− q)P T rs = 0 (30)
which yields the best response function
QTg =q(Ag + P T )− (1− q)P T rs −Q−i,T
b
2(31)
Assuming again that all firms are symmetric, we set Q−i,Tg = (n− 1)QTg and solve for the
optimal quantity that the retailer offers in the good state which is
QTg =(Ag − P T )q − (1− q)P T rs
n+ 1(32)
According to Equation (10), the first order condition to solve P T and rs is:
∂
∂P T
[qP TQTg + (1− q)
(P TQTb +
rsPT (QTg −QTb )1 + r
)]= 0 (33)
∂
∂rs
[qP TQTg + (1− q)
(P TQTb +
rsPT (QTg −QTb )1 + r
)]= 0 (34)
By substituting the optimal quantities, QTb , QTg , that the retailer offers in a bad state
and a good state, respectively and solving the partial derivative, Equations (33) and (34)
become
Ab(1− q)q(1− rs) +Agq(q + rs − qrs)− 2P T (q + (1− q)r2s)n+ 1
= 0 (35)
P T (1− q)[(Ag −Ab)(1− q) + 2P T rs]
(n+ 1)q= 0 (36)
Simultaneously solving Equations (35) and (36) yields the price and trade credit interest
rate charged by a supplier under trade credit financing,
P T =2(qAg + (1− q)Ab)
3 + n(37)
rs =q(Ag −Ab)
qAg + (1− q)Ab(38)
By substituting the equilibrium price and trade credit interest rate into the Equation (28)
51
and Equation (32), the quantities sold in the good state and the bad state are Agn+3 and Ab
n+3 ,
respectively.
Proof of Proposition 3Proof. The marginal cost in the bad state
At the optimal quantity determined by the first order condition of Equation (2), the
marginal revenue (MRb) from selling one more unit must equal the total marginal cost
(MCb), which we can write as the sum of the marginal purchasing (MPC) and marginal
financing costs (MFCb),
MRb =MCb =MPC +MFCfb . (39)
Under both forms of financing marginal revenue and marginal purchase costs are given by
MRs = As − 2Qfs −Q−i,fs , and MPC = P f , respectively.
Under bank financing, Equation (39) becomes
MCBb = PB +MFCBb (40)
The marginal financing cost is zero in the bad state, thus, the marginal cost is equal to
PB.
Under trade credit financing, Equation (39) becomes
MCTb = P T +MFCTb (41)
The marginal financing cost is − PT rs(1+r) in the bad state, thus, the marginal cost is equal
to P T − PT rs(1+r) ,since PB = P T at the equilibrium, the marginal cost under trade credit is
lower in the bad state.
The marginal cost in the good stateRearrange Equation (98), it becomes
MCg =MPC +MFCfg +(1− q)q
MFCfb . (42)
under bank financing, the marginal cost is equal to PB since the marginal financing costs
in both states are zero by assuming r = 0.
Under trade credit financing, the marginal product cost is P T , the marginal financing
cost in the good state is 0; and the marginal financing cost in the bad state is (1−q)q
PT rs(1+r) ,
thus the marginal cost in a good state is P T (1 + (1−q)q
rs(1+r)). Again, as PB = P T at the
equilibrium, the marginal cost under trade credit is higher in a good state.
52
Proof of Corollary 1Proof. As rs =
q(Ag−Ab)qAg+(1−q)Ab , thus the partial derivative with respect to q is given by
∂rs∂q
=Ab(Ag −Ab)
(qAg + (1− q)Ab)2> 0 (43)
and the partial derivative with respect to (Ag −Ab) is given by
∂rs∂(Ag −Ab)
=q
qAg + (1− q)Ab> 0 (44)
Proof of Proposition 5Proof. By using the solutions obtained from Proposition 1 and Proposition 2, we have
the explicit solutions of supplier and retailer’s profits as well as consumer surplus for both
bank financing and trade credit financing cases. Under bank financing, by substituting the
equilibrium price, quantities sold by the retailer in both good and bad states into Equation
4 and 6, the profits obtained by the retailer and the supplier as well as the total producer
surplus are shown as:
ωB =1
(1 + n)2(3 + n)2[A2
g(9 + n2 + n(6− 4q)− 8q)q −
8AgAb(2 + n)(1− q)q +A2b(1− q)(1 + n2 + 8q + n(2 + 4q)] (45)
πB =2(Ab(1− q) +Agq)
2
(3 + n)2(46)
ωB + πB =1
(1 + n)2(3 + n)2[A2
g(9 + 6n− 6q + n2(1 + 2q)) +
4AgAb(n2 − 3)(1− q) +A2
b(1− q)(3 + 6n+ 6q + n2(3− 2q)] (47)
Similarly, under trade credit financing, by substituting the equilibrium price, trade credit
interest rate and quantities sold by the retailer in both good and bad states into Equation 4
and 7, the profits obtained by the retailer and the supplier as well as the total producer
surplus are shown as:
ωT =A2b(1− q) +A2
gq
(3 + n)2(48)
53
πT =2(A2
b(1− q) +A2gq)
(3 + n)2(49)
ωT + πT =3(A2
b(1− q) +A2gq)
(3 + n)2(50)
Thus, the difference of producer surplus between trade credit financing and bank fi-
nancing is
(ωT + πT )− (ωB + πB) =2(Ag −Ab)2(n2 − 3)(1− q)q
(3 + 4n+ n2)2(51)
From the above equation, we can find that when n = 1 (one supply chain or monopoly
industry), the total producer surplus is smaller under trade credit financing than bank financ-
ing; however, if n ≥ 2 (at least two supply chains or duopoly industry), the total producer
surplus is greater under trade credit financing than bank financing.
Proof of Proposition 4Proof. For Equation (51), we take the partial derivative with respect to n, and then the first
order condition is shown as:
∂[(ωT + πT )− (ωB + πB)]
∂n=
4(Ag −Ab)2(12 + 9n− n3)(1− q)q(3 + 4n+ n2)3
(52)
then, when n = 1,we have ∂[(ωT+πT )−(ωB+πB)]∂n =
88(Ag−Ab)2(1−q)q3375 > 0 and when
n = ∞, then ∂[(ωT+πT )−(ωB+πB)]∂n = 0. From this finding, we can see that the partial
derivative is rising initially when n is very small but declines when n becomes very large,
therefore, there exists an inverse U-shaped relationship between the advantage of trade
credit financing and the number of supply chains.
B Deviation by a supply chain
We extend the basic model in the paper assuming that m supply chains with bank financing
compete with (n-m) supply chains using bank financing. We allow the two types of supply
chains to follow different strategies in the product market. We solve for the subgame per-
fect Nash equilibrium by backward induction starting with the retailers’ decision problem.
Compute the trade-off for the supply chain using bank financing.
Stage 3: One of m retailers’ end of period problem —ex-post competition in a bad state
At the end of the period, each retailer imaximizes its profit ωBb by competing in quantity
54
QBb . The retailer’s problem is
maxQBb
ωBb = (Ab − (m− 1)QOBb − (n−m)QTb −QBb )QBb − (rPBQBg + PBQBb ) (53)
According to Equation (53), the first order condition to solve QBb is
∂
∂QBb
[(Ab − (m− 1)QOBb − (n−m)QTb −QBb )QBb − (rPBQBg + PBQBb )
]= 0 (54)
Solving the partial derivative, Equation (54) becomes
Ab − PB − 2QBb − (n−m)QTb − (m− 1)QOBb = 0 (55)
which yields the best response function
QBb =1
2(Ab − PB + (n−m)QTb − (m− 1)QOBb ) (56)
Stage 2: One of m retailers’ ex-ante inventory decision
We first define the profit in the good state under bank financing, ωBg ,
ωBg = (Ag − (m− 1)QOBg − (n−m)QTg −QBg )QBg − (rPBQBg + PBQBg ) (57)
and then compute the ex-ante expected profit:
maxQBg
[(1− q)ωBb + qωBg
](58)
According to Equation (58), the first order condition to solve QBg is
∂
∂QBg
[(1− q)ωBb + qωBg
]= 0 (59)
By substituting the optimal quantity that the retailer offers in the bad state, QBb , and
solving the partial derivative, Equation (56) becomes
q(Ag − PB − 2QBg − (n−m)QTg − (m− 1)QOBg )− PBr = 0 (60)
which yields the best response function
QBg =1
2(Ag − PB − (n−m)QTg − (m− 1)QOBg )− PBr
2q(61)
55
Stage 1: the supplier decides on the price
Under bank financing, each supplier only has the wholesale price as a choice variable
to maximize their expected profits
maxPB
πB = (1 + r)PBQBg − (1− q)PB(QBg −QBb ) (62)
According to Equation (62), the first order condition to solve PB is:
∂
∂PB[(1 + r)PBQBg − (1− q)PB(QBg −QBb ))
]= 0 (63)
By substituting the optimal quantities, QBb , QBg , that the retailer offers in a bad state
and a good state, respectively, and solving the partial derivative and setting it equal to zero,
the price charged by a supplier under bank financing is:
PB =1
2(q + 2qr + r2)[Ag(q+r)+Ab(1−q)−(n−m)((1−q)QTb +(q+r)QTg )+(m−1)((1−q)QOBb +(q+r)QOBg ]
(64)
Then compute the trade-off for the supply chain using trade credit financing.
Stage 3: One of n-m retailers’ end of period problem —ex-post competition in a bad
state
At the end of the period, each retailer imaximizes its profit ωTb by competing in quantity
QTb . The retailer’s problem is
maxQTb
ωTb = (Ab−mQBb −(n−m−1)QOTb −QTb )QTb −(P TQTb +P T rs(QTg −QBb )/(1+r))
(65)
According to Equation (65), the first order condition to solve QTb is
∂
∂QTb
[(Ab −mQBb − (n−m− 1)QOTb −QTb )QTb − (P TQTb + P T rs(Q
Tg −QTb )/(1 + r))
]= 0
(66)
Solving the partial derivative, Equation (66) becomes
Ab − P T −mQBb − 2QTb − (n−m− 1)QOTb − P T rs/(1 + r) = 0 (67)
which yields the best response function
QTb =1
2(Ab − PB −mQBb + (n−m− 1)QOTb − P T rs/(1 + r)) (68)
Stage 2: One of m retailers’ ex-ante inventory decision
56
We first define the profit in the good state under trade credit financing, ωTg ,
ωTg = (Ag −mQOBg − (n−m− 1)QOTg −QTg )QTg − P TQTg (69)
and then compute the ex-ante expected profit:
maxQTg
[(1− q)ωTb + qωTg
]= 0 (70)
According to Equation (70), the first order condition to solve QTg is
∂
∂QTg
[(1− q)ωTb + qωTg
]= 0 (71)
By substituting the optimal quantity that the retailer offers in the bad state, QTb , and
solving the partial derivative and setting it equal to zero, the inventory the retailer chooses
is:
QTg =1
2[Ag − P T −mQBg − (n−m− 1)QOTg )− P T rs(1− q)
q(1 + r)] (72)
Under trade credit financing, each supplier maximizes the expected profit through si-
multaneous choice of price P T and trade credit interest rate rs.
maxPT ,rs
πT = qP TQTg + (1− q)
(P TQTb +
rsPT (QTg −QTb )1 + r
)(73)
According to Equation (10), the first order condition to solve P T and rs is:
∂
∂P T
[qP TQTg + (1− q)
(P TQTb +
rsPT (QTg −QTb )1 + r
)]= 0 (74)
∂
∂rs
[qP TQTg + (1− q)
(P TQTb +
rsPT (QTg −QTb )1 + r
)]= 0 (75)
By substituting the optimal quantities, QTb , QTg , that the retailer offers in a bad state and
a good state, respectively and solving the partial derivative and then simultaneously solving
Equations (74) and (75) yields the price and trade credit interest rate charged by a supplier
under trade credit financing,
P T =q(1 + r)
2q(1 + r)2 + 2(1− q)r2s[Ab(1−q)+Agq−m(1−q)QBb −mqQBg −(n−m−1)QOTb ]
(76)
57
rs =q(1 + r)
2P T 2(1− q)[Ag −Ab + (n−m− 1)(QOTg −QOTb )−m(QBg −QBb )] (77)
Solving all equations yields
rs =(Ag −Ab)(3 + n)q
(n+ 2m+ 3)(Agq −Ab(1− q))(78)
P T =2(Agq +Ab(1− q))
(n+ 3)(79)
QTg =Ag(n+ 2mq + 3) + 2Abm(1− q)
(n+ 2m+ 3)(n+ 3)(80)
QTb =2Agmq +Ab(n+ 3 + 2m(1− q))
(n+ 2m+ 3)(n+ 3)(81)
PB =2(Agq +Ab(1− q))
(n+ 3)(82)
QBg =Ag(n(3− 2q)− 2(m− 3)q + 9) + 2Ab(n−m+ 3)
(n+ 2m+ 3)(n+ 3)(83)
QBb =Ab((n+ 3)(1 + 2q) + 2m(1− q))− 2Ag(n−m+ 3)q
(n+ 2m+ 3)(n+ 3)(84)
Given the results obtained above, we can calculate the producer surplus for one supply
chain deviating to bank financing and we compare the difference with the producer sur-
plus under trade credit financing and the difference is: 6(Ag−Ab)2(1−q)q(n(n+4)+1)(n+3)2(n+5)2
, which is
positive, meaning that one-time deviation for a supply chain is beneficial; however, if we
compare the benefit from deviation in terms of producer surplus under trade credit financ-
ing, the benefit is very small. A detailed Mathematica file with all results is available from
the authors upon request.
C Classic collusion—the Integrated Monopolist
Start with considering an integrated monopolist. Assume that the firm produces goods at a
marginal cost of zero at the beginning of each period. The firm then sells the goods at the
end of the period. Since goods cost zero to produce, no financing is needed for production.
We know that the solution is to sell Ab2 in the bad state and Ag
2 in the good state. If we
58
assume n identical vertically integrated supply chains collude together, then each supply
chain sells Qb = Ab2n in the bad state and Qg =
Ag2n in the good state—we refer to this
case as classic collusion in the paper. What is the incentive to deviate from this collusive
equilibrium?
The deviating supply chain sales in a bad state
At the end of the period, each retailer imaximizes its profit ωBb by competing in quantity
QBb . The retailer’s problem is
maxQb
ωb = (Ab −Qb − (n− 1)QOb )Qb (85)
Solving the partial derivative with respect to Qb, which yields the best response func-
tion:
Qb =1
2(Ab + (n− 1)QOb ) (86)
Similarly in the good state the best response function is:
Qg =1
2(Ag + (n− 1)QOg ) (87)
Assuming the other firms still stick to the cartel output, i.e.: QOg =Ag2n in a good state
and QOb = Ab2n in a bad state, then the optimal sales for the deviating firm in a bad state are
Qb =Ab(n+1)
4n and Qg =Ag(n+1)
4n in a good state, respectively. According to the sales, the
ex-ante expected profit i.e. (1− q)ωBb + qωBg for the deviating firm is (A2gq+A
2b(1−q))(n+1)2
16n2 .
D Expected quantities sold
For a large set of parameters expected sales for the supplier are larger under trade credit
financing than under bank financing. In the left panel of Figure 8 we show the region of
the parameter space where the expected number of goods sold, qQfg +(1− q)Qfb , is higher
for trade credit financing. Unless the difference between the good state and the bad state is
small or the probability of the good state is very low the number of goods sold under trade
credit exceed those under bank financing. The region of the parameter space where this is
true increases as interest rates decrease.
For expected sales in dollar terms (right panel) the result is stronger. Here expected
sales for the supplier, P f (qQfg + (1 − q)Qfb ) under trade credit financing exceed sales
under bank financing unless the difference between states is extremely large and the good
state is very unlikely.
59
0.0 0.2 0.4 0.6 0.8 1.0
20
40
60
80
100
0.0 0.2 0.4 0.6 0.8 1.0
20
40
60
80
100
Chokeprice
badstate
Ab
Probability good state q
Chokeprice
badstate
Ab
Probability good state q
r = 0.02
r = 0.05
r = 0.10
r = 0.02
r = 0.05r = 0.10
Figure 8. Region where expected sales under trade credit exceed those of bank financing. Theregions indicate for which parameter values expected sales in number of goods (left) and in dollar terms(right) under trade financing are larger than under bank financing. The parameters for the graph areunless otherwise specified: Ag = 100, n = 5.
E Banks mimicking the trade credit contract
If the trade credit contract is a beneficial collusion mechanism, why can the same arrange-
ment not be replicated through state contingent bank financing? Start by observing that the
provision of trade credit financing is not a zero NPV project for the supplier. In the limiting
case when r = 0, which is analyzed through most of the paper, it is easy to see that a posi-
tive trade credit interest rate will result in a positive contribution to the supplier’s profit. It
is easy to find other parameters, like when the probability of the bad state is very low and
r is high, under which providing free financing in the good state is on average costly for
the supplier. Figure 9 shows the expected profit of the supplier from providing trade credit
financing, which is the value of the unsold inventory, P (Qg − Qb), times the trade credit
interest rate, which is paid in the bad state and one period later, minus the opportunity cost
of providing free financing for the value of the inventory, rPQg:
((1− q)rs(Qg −Qb)
1 + r− rQg
)P
The expected payoff from trade credit is declining in the risk-free rate as a higher interest
rate makes the free financing period more costly for the supplier. Price discrimination is
more profitable when both states occur with equal probability and so is trade credit financ-
ing (left panel). The same is true when the difference between the good state and the bad
state is more pronounced, i.e. lower Ab (right panel).
The nonzero NPV of the trade credit contract makes it harder to replicate by the banking
60
0.02 0.04 0.06 0.08 0.10
-20
-15
-10
-5
5
10
0.02 0.04 0.06 0.08 0.10
-10
10
20
30
Expectedprofitfrom
tradecreditfinance
Risk free interest rate r
Expectedprofitfrom
tradecreditfinance
Risk free interest rate r
q = 1/2q = 1/4
q = 3/4
Ab = 35
Ab = 50
Ab = 65
Figure 9. Expected per period profit for the supplier from providing trade credit financing. Theparameters for the graph are unless otherwise specified: Ag = 100, Ab = 60, q = 1/2, n = 3.
sector for three reasons: first, when the supplier then sets the wholesale price P she will
take the profits from financing into account and will set a different price than when all
financing cash flows go towards outside financiers. Second, the positive or negative NPV
of the financing component makes it hard for a competitive banking sector to replicate
exactly the trade credit contract. If the NPV was positive, it would get competed away, if
the NPV from trade credit financing was negative, the banking sector would not offer such
a contract.
Finally, a trade credit style financing contract provided by a competitive banking sector
is much less robust to deviation from the collusive equilibrium than trade credit provided
by the supplier. Unless banks and retailers can form a long-lasting committed relationship
for reasons outside the model retailers have an incentive to deviate in the bad state. Suppose
that a bank replicates the trade credit contract and offers a low interest rate in the good state
and asks for a high interest rate in the bad state. The retailer could deviate in the bad state
and borrow from another bank. Since the retailer can never default, he can borrow funds
from a new bank at the risk-free rate and repay the old bank instead of paying the penalty
rate on the unsold inventory. To prevent such a deviation the bank and the financier would
have to write a binding, long-term contract or build a long-lasting relationship for reasons
outside of the model, otherwise there are no repercussions in a competitive banking sector.
Such a deviation is less of a concern under the trade credit mechanism analyzed in the main
section of this paper. Should a retailer deviate to bank financing to avoid the penalty rate
in the bad state the supplier will not provide trade credit financing going forward, the bank
financing equilibrium would be implemented, resulting in a lower producer surplus.
Suppose that still all three obstacles could somehow be overcome. Assume that for
reasons outside of the model the retailer can enter a committed lending relationship with
a bank who offers, similar to a trade credit contract, a rate of rL ≥ 0 if the inventory is
61
0.02 0.04 0.06 0.08 0.10
400
450
500
550
ProducerSurplus
Interest rate in the good state rL
TC-contract n = 3
Relationship bank n = 3
TC-contract n = 4
Relationship bank n = 4
Figure 10. Producer surplus under trade credit financing and under a hypothetical contract withstate contingent interest rates offered by competitive outside financiers as a function of the interestrate offered in the good state. The parameters for the graph are: Ag = 100, Ab = 60, q = 1/2, r =0.05.
sold within the period and charges rH > rL to finance any unsold inventory. Furthermore,
assume that the bank sets the two interest rates such that its expected profit is zero to address
the first two concerns mentioned above. Note that the game differs from the model in the
main part of the paper as the supplier cannot obtain any gains from financing and will
therefore set a different price.
We are not able to solve such a model analytically but we found, for all parameters that
we analyzed, the producer surplus to be lower than under a traditional trade credit contract.
Figure 10 shows an example for three and four firms, respectively. The graph shows the
producer surplus under trade credit financing and under the forced relationship banking
contract for different values of the interest rate in the good state, rL. The interest rate in the
bad state is then set such that outside investors break even in expectation. The trade credit
contract results in a higher producer surplus than the relationship banking contract.
F Decomposing the trade credit benefit
Define the number of supply chains n where retail prices under bank and trade credit fi-
nancing are equidistant from the retail price of an integrated monopolist in the good state
as n∗g. Since the demand function is linear, we formulate the problem in term of aggre-
gate quantities. The average of the aggregate quantities offered in the good state under
bank financing, nQBg , and under trade credit, nQTg , has to equal the quantity the integrated
monopolist would offer, Ag/2.
nQBg + nQTg2
=Ag2
(88)
62
Substituting forQBg andQGg from Proposition 1 and 2, respectively, and solving for n yields
a quadratic equation in n where we only consider the positive solution, which is
n∗g =Ab(1− q) +Agq +
√3Ag
2 + (Ab(1− q) +Agq)2
Ag(89)
The same approach for the bad state leads to
n∗b =Ab(1− q) +Agq +
√3Ab
2 + (Ab(1− q) +Agq)2
Ab(90)
Because the choke price in the good state is higher than in the bad state. Ag > Ab,
it is easy to show that n∗g < n∗b . Because Ag > 0, Ab > 0, and 0 < q < 1 it is also
straightforward to see that n∗g > 0. Therefore there always exists a region, 0 < n <
n∗g where any benefit of trade credit over bank financing only comes from the bad state
followed by a region n∗g < n < n∗b where trade credit financing is beneficial in both states.
There is an upper limit for n∗g. Note that since Ag > Ab, n∗g is increasing in q. Setting
q = 1 and simplifying yields n∗g ≤ 3. There is, however, no upper limit for n∗b . Set
Ab = 2Agq/(2q + n + 1) so that Assumption (1) is binding and substitute into Equation
(90). Simplifying yields n∗b = (3 + n +√21 + 6n+ n2)/2 which goes to infinity when
n becomes large. Intuitively in the region close to where Assumption (1) is binding sales
under bank financing in the bad state are close to zero, as the retail price is close to the
wholesale price and retailers do not find it worthwhile to offer the product to the market.
The trade credit penalty causes retailers to accept retail prices that are below the wholesale
price to avoid the penalty. They offer a positive quantity to the market at a loss to them but
still at a profit for the supply chain as the production cost is zero. If n∗b is finite, as in most
cases and as in the examples plotted in Figure 2, there exists a third region of the parameter
space where for n > n∗b trade credit financing only creates more producer surplus than
bank financing in the good state.
G Emergence of trade credit
In the main body of the paper we compare pure bank financing of inventory with pure trade
credit financing. In this section we analyze one possible explanation for the emergence
of trade credit by analyzing the stability of the bank financing equilibrium. Given that all
other supply chains use bank financing, we find that when the risk-free rate is positive, one
supply chain benefits from deviating and offering a small amount of trade credit financing,
making the pure bank financing equilibrium inherently unstable.
63
Intuitively providing a bit of trade credit financing will not change the retailers product
market behavior directly. When the amount of trade credit financing is small the marginal
good sold in both, the good and the bad state, is still financed by a bank loan. For the
supplier, however, even a small amount of trade credit financing will change the optimal
wholesale price. While cash sales are paid to the supplier at the beginning of the period,
trade credit sales are settled at the end of the period. The supplier, when providing free
financing, effectively forgoes interest on any trade-credit-financed revenue. Because the
sales proceeds cannot be invested to earn interest the marginal gain from raising the whole-
sale price is lower under partial trade credit financing than under bank financing, which will
cause the supplier to optimally set a lower wholesale price than under pure bank financing.
The lower wholesale price, in turn, makes the retailer of the partially trade credit financed
supply chain more aggressive and the optimal response of the other supply chains is to re-
duce the quantities offered. The deviating supply chain will thus capture a larger market
share at the expense of its rivals. As we will more formally show below an individual sup-
ply chain can increase its producer surplus by offering a bit of trade credit financing given
that all other supply chains use pure bank financing.
Assume that out of the n supply chains in the economy n − 1 use pure bank financing
while one supply chain considers to finance ι < Qb units with trade credit. Note that
we only look at cases where the amount of trade-credit-financed goods is smaller than the
amounts of goods sold in the bad state, so firms can always – even in the bad state – repay
the supplier and a trade credit penalty will never be realized. Therefore the trade credit
interest rate is irrelevant.
Start with the n − 1 supply chains that use only bank financing. The retailers problem
in the bad state will determine the quantity offered in the bad state, Qb, and is similar to
the pure bank financing case in Equation (4) with the notable exception that he must take
into account that the firm that relies on partial trade credit financing might use a different
product market strategy and will offer a quantity Qιb in the bad state:
maxQb
ωb = (Ab −Qb −Q−ib −Q
ιb)Qb − PQb − PQgr (91)
where Q−ib no represents the aggregate output offered by the n − 2 other retailers that use
pure bank financing.
Analogous to Equation (5) the retailer earns in the good state
ωg = (Ag −Qg −Q−ig −Qιg)Qg − PQg − PQgr.
64
and will as in Equation (8) determine his optimal inventory based on expected profit solving
maxQg
ω = [(1− q)ωb + qωg] (92)
The supplier will maximize expected profit as in Equation (9), which will determine the
wholesale price P .
maxP
π = (1 + r)PQg − (1− q)P (Qg −Qb) (93)
The deviating supply chain finances ι units of the good with trade credit. In the bad
state the goods on trade credit are always repaid first and since we assume that ι is less than
the units sold in the bad state, no penalty is realized. The partial trade credit makes the
retailer better off by providing partial free financing. The retailer only has to pay interest
on the bank financed portion of his inventory, P ι(Qιg − ι). Since the marginal good sold
in both states is financed by the bank, partial trade credit financing will not influence the
retailer’s optimal sales directly. However, as we will see below, partial trade credit financing
will change the financing cost of inventory which will impact the retailer’s optimal product
market strategy. The corresponding equations for the retailer in the deviating supply chain
are
maxQιb
ωιb = (Ab −Qb −Q−ib −Q
ιb)Q
ιb − P ιQιb − P ι(Qιg − ι)r (94)
ωιg = (Ag −Qg −Q−ig −Qιg)Qιg − P ιQιg − P ι(Qιg − ι)r.
maxQιg
ωι =[(1− q)ωιb + qωιg
](95)
The supplier of the deviating supply chain will carry the cost of free trade credit fi-
nancing. She will collect payment on the goods financed on trade credit, P ιι, at the end of
the period while she will collect the payment on bank financed goods, P ι(Qιg − ι), at the
beginning of the period and can hence collect interest on the latter.
maxP ι
πι = (1 + r)P ι(Qιg − ι) + P ιι− (1− q)P ι(Qιg −Qιb) (96)
When ι = 0 the problems of the two types of supply chains become identical and
the solution collapses to the pure bank financing equilibrium. We solve the first order
conditions corresponding to the six optimization problems (91)-(96) and assume symmetry
65
amongst all pure bank financed firms to get:32
Qb =3Ab
(2(n+ 3)qr + q(n+ 2q + 1) + (n+ 3)r2
)− 6Agq(q + r)− 2ι(n+ 1)qr
3(n+ 1)(n+ 3) (2qr + q + r2),
Qg =6Ab(q − 1)(q + r) + 3Ag
(2(n+ 1)qr + q(n− 2q + 3) + (n+ 1)r2
)− 2ι(n+ 1)r(q + r)
3(n+ 1)(n+ 3) (2qr + q + r2),
P =2q(−3Ab(q − 1) + 3Ag(q + r)− 2ιr)
3(n+ 3) (2qr + q + r2),
Qιb =3Ab
(2(n+ 3)qr + q(n+ 2q + 1) + (n+ 3)r2
)− 6Agq(q + r) + 2ι(n+ 1)(n+ 2)qr
3(n+ 1)(n+ 3) (2qr + q + r2),
Qιg =6Ab(q − 1)(q + r) + 3Ag
(2(n+ 1)qr + q(n− 2q + 3) + (n+ 1)r2
)+ 2ι(n+ 1)(n+ 2)r(q + r)
3(n+ 1)(n+ 3) (2qr + q + r2),
Pι =2q(3Ab(1− q) + 3Ag(q + r)− ι(n+ 5)r)
3(n+ 3) (2qr + q + r2)
We plug the above solution into the profit of the supplier and retailer and add them to
obtain the producer surplus. Our main interest is to find out if the deviating supply chain
has an incentive to supply trade credit given that all other supply chains use bank financing.
We compute the gain for the deviating supply chain from offering an infinitesimal amount
of trade credit financing given that all other supply chains use bank financing.
∂(ωι,∗ + πι,∗)
∂ι
∣∣∣∣ι=0
=2(n+ 1)qr(Ab(1− q) +Ag(q + r))
(n+ 3)2 (2qr + q + r2)> 0 (97)
We can see that the bank financing equilibrium is not stable. Each supply chain has
an incentive to offer some trade credit financing to their retailer. This is one potential
explanation for the existence of trade credit. Once trade credit exists supply chains might
find it easier to collude on a trade credit financing equilibrium as analyzed in the paper.
H Trade credit and state specific marginal costs
We will show that sales are always bound by inventory in good states and that constraint (3)
is binding. The retailer’s quantity choice in good states is therefore made when he chooses
inventories before the state of demand is realized.
We can rewrite the first order condition of Equation (8) for the retailer’s optimal level
of inventory as
qMRg = qMCfg = q(MPC +MFCfg ) + (1− q)MFCfb . (98)
32A Mathematica workbook with the details on the derivation is available from the authors upon request. Ev-erything can be solved closed form but the expressions are long and provide no intuitive insights.
66
The retailer obtains a marginal revenue, MR, from an increased unit of inventory only
in the good state which occurs with probability q because not all of the inventory is sold in
a bad state. Increasing inventory incurs two ex-ante marginal costs: the marginal cost of
purchasing (MPC) and financing (MFC) the additional good when it gets sold in the good
state and the marginal cost of financing the additional good in the bad state when it stays
in inventory. The marginal revenue and purchase costs are MRs = As − 2Qfs − Q−i,fs ,
and MPC = P f . Under bank financing, the ex-ante marginal financing cost equals to
the interest paid for the value of the additional good in both demand states, MFCBg =
MFCBb = rPB . Substituting into Equation (98) we get qMCBg = q(PB + rPB) + (1−q)rPB. The total marginal cost is then MCBg = PB(1 + 1
q r).
Under trade credit financing, the retailer gets free financing for the good state in which
all goods are sold but has to finance the unsold goods at the trade credit interest rate in the
bad state: MFCTg = 0, MFCTb = P T rs/(1 + r) and MCTg = P T (1 + rs1+r
1−qq ).
In good states, if we were to ignore the inventory constraints, the retailer’s optimal level
of sales should be given by MRg = MCfg . Comparing to the inventory decision problem,
the retailer would choose to sell more than the inventory under both bank financing and
trade credit financing. The shadow price of the inventory is r 1qPB and rs
(1+r)1−qq P T , for
bank financing and trade credit financing, respectively. The retail competition in good states
therefore is softened under both financing schemes. However, there are two differences
between bank financing and trade credit financing. First, rs is a choice variable optimally
set by the supplier while r is exogenously given. As a result, the trade credit financing
scheme enables the supplier to strategically influence her retailer’s aggressiveness in both
demand states, specifically how much to intensify the competition in a bad state and how
much to soften the competition in a good state. Second, under trade credit financing, rsexplicitly reduces the marginal cost in bad states and increases the marginal cost in good
states, while r does not have an explicit effect on the marginal cost in the bad state under
bank financing.
There are potentially two stages of price discrimination. First, retailers price discrim-
inate against consumers in different states of demand. Second, and the main focus of this
paper, the suppliers price discriminate against their retailers. Trade credit financing im-
plicitly allows the supplier to charge the retailer state contingent marginal costs and thus
price discriminate between demand states. On appearance, the supplier seems to charge the
retailer a low price (free financing) in good states and a high price (due to a higher trade
credit interest rate) in bad states, which seems to contradict the typical pricing pattern in
price discrimination theory: a high (low) price is charged when a demand is high (low). To
find the correct state contingent prices rewrite the supplier’s expected costs as:
67
qP TQTg + (1− q)
(P TQTb +
rsPT (QTg −QTb )1 + r
)
=
(qP TQTg + (1− q)
rsPTQTg
1 + r
)+
((1− q)
(P TQTb −
rsPTQTb
1 + r
))
= q
(P T +
1− qq
rsPT
1 + r
)QTg + (1− q)
(P T − rsP
T
1 + r
)QTb
= qP Tg QTg + (1− q)P Tb QTb
where P Tg = P T (1 + 1−qq
rs1+r ) and P Tb = P T (1 − rs
1+r ) are the supplier’s effective
prices in good and bad states, respectively. The price charged by the supplier in the good
state is clearly higher than that in the bad state. Notice that P Tg and P Tb are exactly the
retailer’s total marginal costs for the equilibrium sales in good and bad states, respectively.
The incentive for a supplier to provide trade credit is hence to price-discriminate to her
retailer between strong and weak demand states. In our model the rationale for a supplier
to set state contingent prices is to change the marginal cost for the retailer to influence
his behavior in the final product market. The supplier’s price discrimination in our anal-
ysis is a double price discrimination, or a price discrimination to influence the retailer’s
price discrimination against the consumers. We summarize our findings in the following
proposition:
Proposition 6 Under trade credit financing, the supplier optimally price discriminates the
retailer between the states of demand: charging a high effective price P Tg = P T (1 +1−qq
rs1+r ) in good states and a low effective price P Tb = P T (1 − rs
1+r ) in bad states. As a
result, compared to bank financing, the profits of the supplier are higher under trade credit
financing.
I Trade credit as double marginalization problem
Figure 11 illustrates the basic mechanism of our model by means of an example. The graph
shows the marginal cost curves under trade credit and bank financing (horizontal lines), the
inverse demand curve (bold line), and the marginal revenue for the integrated monopolist.
Each point in the line labeled ”equilibrium marginal revenue oligopoly” corresponds to an
equilibrium in a Cournot oligopoly game with three firms and shows the marginal revenue
(along the vertical axis) and aggregate output (along the horizontal axis) in that equilibrium.
To derive this line we solve a simple Cournot game for marginal costs ranging from zero to
68
P
∑Qg
∑Qb
Good stateBad state
PM = PT
M
T
Ag
PO
O
P = MCB
MCTg
B
PB
MR
gintegrated
monop
olist
equilibriumMRgoligopoly
PM = PT
Ab
M
TPO
O
P = MCB
PB
B
MCTb
Figure 11. Product market equilibria, marginal revenues and costs under alternative financingarrangements. The graph shows the inverse demand curve (bold line), the marginal revenue of theintegrated monopolist, and the equilibrium marginal revenue line for an oligopoly, for which each pointcorresponds to an equilibrium in an oligopoly game and represents the marginal revenue and aggregatesupply in that equilibrium. The point M , O , B, and T denote the equilibrium points where marginalrevenue equals marginal cost of the integrated monopolist, the integrated oligopolist, the n supply chainsunder bank financing, and the n supply chains under trade credit financing, respectively. The parametersfor the graph are: Ag = 10, Ab = 7, q = 1/2, r = 0, n = 3.
the choke price. We then plot for each equilibrium a point defined by marginal revenue and
the aggregate output.
We start as a reference case with a single, vertically integrated monopolist. Since pro-
duction cost of the good is assumed to be zero, the optimal quantity that the vertically
integrated monopolist offers can be found where the marginal revenue line hits the x-axis
(point M ) and the corresponding price in the consumer product market is given by PM .
When more vertically integrated firms enter the industry, competition flattens the equilib-
rium marginal revenue curve under oligopoly and integrated firms offer more in aggregate
(point O) which decreases their equilibrium revenue as products in the consumer market
are sold for PO.
The retailers of an oligopoly supply chain face the same marginal revenue function but
their marginal costs increase because they have to purchase the intermediate goods at the
wholesale price P from the supplier. When r goes to zero, as in the example of the graph,
69
the retailers – using bank financing – pay no financing costs and thus their marginal cost
equals the price set by the supplier, P , and the overall equilibrium in the product market is
at point B. The aggregate output of the supply chain comes closer to the quantity that is
offered by the vertically integrated monopolist, however under bank financing we see that
relative to the integrated monopolist the output is too high in the good state and too low
in the bad state, respectively. This is exactly the problem that trade credit can overcome.
By optimally choosing the trade credit interest rate, the supplier can increase her retailer’s
marginal cost in the good state to MCTg and lower the marginal cost in the bad state to
MCTb . In some cases it is possible – as in this specific example – to achieve exactly the
output of a vertically integrated monopolist. In general, trade credit financing, with its
ability to charge state dependent marginal costs, can make the retailer choose an output
closer to the output of the integrated monopolist than bank financing, and thereby increase
producer surplus at the expense of consumers.
70
